. . "En th\u00E9orie des graphes, une couverture par cliques ou une partition en cliques d'un graphe non orient\u00E9 est une partition des sommets du graphe en cliques, c'est-\u00E0-dire en des ensembles de sommets \u00E0 l'int\u00E9rieur desquels deux sommets sont adjacents. Un couverture par cliques minimale est une couverture de taille minimale, c'est-\u00E0-dire par un nombre minimal de cliques. Le probl\u00E8me de la couverture par cliques est le probl\u00E8me algorithmique qui consiste \u00E0 trouver une couverture par cliques minimale."@fr . . "Partition en cliques"@fr . . "In graph theory, a clique cover or partition into cliques of a given undirected graph is a partition of the vertices into cliques, subsets of vertices within which every two vertices are adjacent. A minimum clique cover is a clique cover that uses as few cliques as possible. The minimum k for which a clique cover exists is called the clique cover number of the given graph."@en . "In graph theory, a clique cover or partition into cliques of a given undirected graph is a partition of the vertices into cliques, subsets of vertices within which every two vertices are adjacent. A minimum clique cover is a clique cover that uses as few cliques as possible. The minimum k for which a clique cover exists is called the clique cover number of the given graph."@en . "\u5206\u5718\u8986\u84CB\u554F\u984C"@zh . . . "\u0417\u0430\u0434\u0430\u0447\u0430 \u043F\u0440\u043E \u043A\u043B\u0456\u043A\u043E\u0432\u0435 \u043F\u043E\u043A\u0440\u0438\u0442\u0442\u044F"@uk . . . "En th\u00E9orie des graphes, une couverture par cliques ou une partition en cliques d'un graphe non orient\u00E9 est une partition des sommets du graphe en cliques, c'est-\u00E0-dire en des ensembles de sommets \u00E0 l'int\u00E9rieur desquels deux sommets sont adjacents. Un couverture par cliques minimale est une couverture de taille minimale, c'est-\u00E0-dire par un nombre minimal de cliques. Le probl\u00E8me de la couverture par cliques est le probl\u00E8me algorithmique qui consiste \u00E0 trouver une couverture par cliques minimale."@fr . . "17113364"^^ . . . . 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NP-\u043F\u043E\u043B\u043D\u043E\u0442\u0430 \u0437\u0430\u0434\u0430\u0447\u0438 \u043E \u043A\u043B\u0438\u043A\u043E\u0432\u043E\u043C \u043F\u043E\u043A\u0440\u044B\u0442\u0438\u0438 \u0441\u043B\u0435\u0434\u0443\u0435\u0442 \u0438\u0437 \u0441\u0432\u0435\u0434\u0435\u043D\u0438\u044F \u0435\u0451 \u043A \u0437\u0430\u0434\u0430\u0447\u0435 \u0440\u0430\u0441\u043A\u0440\u0430\u0441\u043A\u0438 \u0433\u0440\u0430\u0444\u0430: \u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u0435 \u0433\u0440\u0430\u0444\u0430 \u043D\u0430 \u043A\u043B\u0438\u043A \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u043D\u0430\u0445\u043E\u0436\u0434\u0435\u043D\u0438\u044E \u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u044F \u0432\u0435\u0440\u0448\u0438\u043D \u0434\u043E\u043F\u043E\u043B\u043D\u0435\u043D\u0438\u044F \u043D\u0430 \u043D\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043C\u044B\u0445 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432 (\u043A\u0430\u0436\u0434\u043E\u043C\u0443 \u0438\u0437 \u044D\u0442\u0438\u0445 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432 \u043C\u043E\u0436\u043D\u043E \u043D\u0430\u0437\u043D\u0430\u0447\u0438\u0442\u044C \u043E\u0434\u0438\u043D \u0446\u0432\u0435\u0442, \u0447\u0442\u043E \u0434\u0430\u0441\u0442 -\u0440\u0430\u0441\u043A\u0440\u0430\u0441\u043A\u0443). \u041C\u0438\u043D\u0438\u043C\u0430\u043B\u044C\u043D\u044B\u0439 \u0440\u0430\u0437\u043C\u0435\u0440 \u043A\u043B\u0438\u043A\u043E\u0432\u043E\u0433\u043E \u043F\u043E\u043A\u0440\u044B\u0442\u0438\u044F \u0433\u0440\u0430\u0444\u0430 \u2014 \u043D\u0430\u0438\u043C\u0435\u043D\u044C\u0448\u0435\u0435 \u0447\u0438\u0441\u043B\u043E , \u0434\u043B\u044F \u043A\u043E\u0442\u043E\u0440\u043E\u0433\u043E \u043A\u043B\u0438\u043A\u043E\u0432\u043E\u0435 \u043F\u043E\u043A\u0440\u044B\u0442\u0438\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442. \u0421\u0432\u044F\u0437\u0430\u043D\u043D\u0430\u044F \u0437\u0430\u0434\u0430\u0447\u0430 \u043D\u0430\u0445\u043E\u0436\u0434\u0435\u043D\u0438\u044F \u0447\u0438\u0441\u043B\u0430 \u043F\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043D\u0438\u044F \u0440\u0430\u0441\u0441\u043C\u0430\u0442\u0440\u0438\u0432\u0430\u0435\u0442 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u0430 \u043A\u043B\u0438\u043A, \u0432\u043A\u043B\u044E\u0447\u0430\u044E\u0449\u0438\u0445 \u0432\u0441\u0435 \u0440\u0451\u0431\u0440\u0430 \u0437\u0430\u0434\u0430\u043D\u043D\u043E\u0433\u043E \u0433\u0440\u0430\u0444\u0430; \u044D\u0442\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u0442\u0430\u043A\u0436\u0435 NP-\u043F\u043E\u043B\u043D\u0430."@ru . . "\u8A08\u7B97\u91CF\u7406\u8AD6\u306B\u304A\u3044\u3066\u3001\u6700\u5C0F\u306E\u30AF\u30EA\u30FC\u30AF\u88AB\u8986\uFF08\u30AF\u30EA\u30FC\u30AF\u3072\u3075\u304F\u3001\u82F1: clique cover\uFF09\u3092\u6C42\u3081\u308B\u3053\u3068\u306F\u3001\u30B0\u30E9\u30D5\u7406\u8AD6\u7684NP\u5B8C\u5168\u554F\u984C\u3067\u3042\u308B\u3002\u30AF\u30EA\u30FC\u30AF\u88AB\u8986\u554F\u984C\u306F\u306E1\u3064\u3067\u3001\u305D\u306ENP\u5B8C\u5168\u6027\u306F1972\u5E74\u306E\u8AD6\u6587 \"Reducibility Among Combinatorial Problems\"\uFF08\u300C\u7D44\u5408\u305B\u8AD6\u7684\u554F\u984C\u9593\u306E\u9084\u5143\u53EF\u80FD\u6027\u300D\uFF09\u306B\u793A\u3055\u308C\u3066\u3044\u308B\u3002 \u30AF\u30EA\u30FC\u30AF\u88AB\u8986\u554F\u984C\uFF08\u30AF\u30EA\u30FC\u30AF\u5206\u5272\u554F\u984C\u3068\u547C\u3076\u3053\u3068\u3082\u3042\u308B\uFF09\u3068\u306F\u3001\u4E0E\u3048\u3089\u308C\u305F\u30B0\u30E9\u30D5\u306E\u9802\u70B9\u96C6\u5408\u3092 k-\u500B\u306E\u30AF\u30EA\u30FC\u30AF\u3078\u5206\u5272\u3067\u304D\u308B\u304B\u3092\u6C7A\u5B9A\u3059\u308B\u554F\u984C\u3067\u3042\u308B\u3002\u9802\u70B9\u96C6\u5408\u306E k-\u500B\u306E\u96C6\u5408\u3078\u306E\u5206\u5272\u304C\u4E0E\u3048\u3089\u308C\u305F\u3068\u304D\u3001\u305D\u306E\u5404\u96C6\u5408\u304C\u30AF\u30EA\u30FC\u30AF\u3092\u6210\u3059\u304B\u306F\u591A\u9805\u5F0F\u6642\u9593\u3067\u5224\u5B9A\u3059\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u304B\u3089\u3001\u30AF\u30EA\u30FC\u30AF\u88AB\u8986\u554F\u984C\u306FNP\u306B\u5C5E\u3059\u308B\u3002\u305D\u306ENP\u5B8C\u5168\u6027\u306F\u30B0\u30E9\u30D5\u306E k-\u5F69\u8272\u53EF\u80FD\u6027\u304B\u3089\u306E\u5E30\u7740\u3067\u3042\u308B\u3002\u3053\u308C\u3092\u898B\u308B\u306B\u306F\u3001\u307E\u305A\u30B0\u30E9\u30D5 G \u306E k-\u5F69\u8272\u53EF\u80FD\u6027\u3092\u305D\u306E\u88DC\u30B0\u30E9\u30D5 G\u2032 \u306B\u95A2\u3059\u308B\u4E8B\u5B9F\u306B\u7FFB\u8A33\u3059\u308C\u3070\u3088\u3044\u3002\u3053\u306E\u3068\u304D G \u306E k-\u500B\u306E\u30AF\u30EA\u30FC\u30AF\u3078\u306E\u5206\u5272\u306F G\u2032 \u306E k-\u500B\u306E\u72EC\u7ACB\u96C6\u5408\u3078\u306E\u5206\u5272\u3092\u6C42\u3081\u308B\u3053\u3068\u306B\u5BFE\u5FDC\u3059\u308B\uFF08\u5404\u96C6\u5408\u306B\u305D\u308C\u305E\u308C\u5225\u306E1\u3064\u306E\u8272\u3092\u5857\u308B\u3053\u3068\u3067 k-\u5F69\u8272\u304C\u3067\u304D\u305F\u3053\u3068\u306B\u306A\u308B\uFF09\u3002 \u3053\u306E\u554F\u984C\u3068\u95A2\u9023\u3057\u3066\u3001\u554F\u984C\u306F\u4E0E\u3048\u3089\u308C\u305F\u30B0\u30E9\u30D5\u306E\u8FBA\u3092\u3059\u3079\u3066\u542B\u3080\u3088\u3046\u306A\u30AF\u30EA\u30FC\u30AF\u306E\u96C6\u5408\u3092\u8003\u3048\u308B\u3082\u306E\u3067\u3001\u3053\u308C\u3082\u307E\u305FNP\u5B8C\u5168\u554F\u984C\u3067\u3042\u308B\u3002"@ja . . . "8120"^^ . . . . . "Cobertura clique"@pt . . . . "\u5728\u8A08\u7B97\u8907\u96DC\u5EA6\u7406\u8AD6\u5167\uFF0C\u627E\u4E00\u500B\u6700\u5C0F\u7684\u5206\u5718\u8986\u84CB\uFF08clique cover\uFF09\u662F\u4E00\u500B\u5716\u8AD6\u7684NP\u5B8C\u5168\u554F\u984C\u3002\u9019\u554F\u984C\u5C6C\u65BC\u5361\u666E\u7684\u4E8C\u5341\u4E00\u500BNP-\u5B8C\u5168\u554F\u984C\u4E4B\u4E00\uFF0C\u7531\u5361\u666E\u57281972\u5E74\u7684\u8AD6\u6587\"Reducibility Among Combinatorial Problems\"\u8B49\u660E\u70BANP\u5B8C\u5168\u3002 \u5206\u5718\u8986\u84CB\u554F\u984C\uFF08\u6709\u6642\u53EB\u505A\u5206\u6210\u5206\u5718\uFF0Cpartition into cliques\uFF09\u662F\u554F\u4E00\u500B\u5716\u88E1\u9762\u7684\u6240\u6709\u9EDE\u53EF\u5426\u5206\u6210k\u500B\u3002\u4E00\u65E6\u7D66\u5B9A\u4E86\u9019\u500B\u5716\u8A72\u600E\u9EBC\u5206\u6210k\u500B\u5206\u5718\uFF0C\u6211\u5011\u53EF\u4EE5\u5728\u591A\u9805\u5F0F\u6642\u9593\u88E1\u9762\u6AA2\u8B49\u9019\u500B\u7B54\u6848\u662F\u5426\u6B63\u78BA\uFF0C\u56E0\u6B64\u6211\u5011\u53EF\u4EE5\u77E5\u9053\u9019\u500B\u554F\u984C\u5C6C\u65BCNP\u3002 \u5206\u5718\u8986\u84CB\u554F\u984C\u662FNP\u5B8C\u5168\u9019\u4EF6\u4E8B\u60C5\uFF0C\u53EF\u4EE5\u85C9\u7531\u5C07\u6B64\u554F\u984C\u5F9Ek-\u5716\u8457\u8272\u554F\u984C\uFF08GRAPH k-COLOURABILITY\uFF09\u6B78\u7D04\u51FA\u4F86\u800C\u5F97\u8B49\u3002\u8981\u63A8\u51FA\u9019\u500B\u7D50\u679C\uFF0C\u9996\u5148\u6211\u5011\u5C07\u4E00\u500Bk-\u5716\u8457\u8272\u554F\u984C\u7684\u8F38\u5165\u5716G\u8F49\u6210\u5176\u88DC\u5716G'\u3002\u90A3\u9EBC\uFF0C\u6C42\u51FAG' \u600E\u9EBC\u5206\u51FAk\u500B\u5206\u5718\u9019\u554F\u984C\u5C31\u7B49\u540C\u65BC\u6C42\u51FAG\u600E\u9EBC\u5206\u51FAk\u500B\u7368\u7ACB\u96C6\uFF1B\u6211\u5011\u80FD\u5C07\u6BCF\u500B\u7368\u7ACB\u96C6\u8A2D\u7ACB\u4E00\u500B\u984F\u8272\u4F86\u5F97\u5230k\u500B\u984F\u8272\uFF0C\u4E26\u4E14\u4FDD\u8B49G\u5167\u6240\u6709\u76F8\u540C\u984F\u8272\u7684\u9EDE\u4E0D\u6703\u4E92\u76F8\u9023\u63A5\u3002\u56E0\u6B64\uFF0C\u89E3\u51FAG' \u7684\u5206\u5718\u554F\u984C\uFF0C\u5373\u662F\u89E3\u51FAG\u7684\u8457\u8272\u554F\u984C\u3002\u56E0\u70BA\u6211\u5011\u5DF2\u77E5k-\u8457\u8272\u554F\u984C\u662FNP\u5B8C\u5168\u554F\u984C\uFF0C\u6240\u4EE5\u6211\u5011\u80FD\u85C9\u7531\u5C07\u6240\u6709NP\u7684\u554F\u984C\u5148\u6B78\u7D04\u70BAk-\u8457\u8272\u554F\u984C\uFF0C\u518D\u6B78\u7D04\u70BA\u5206\u5718\u8986\u84CB\u554F\u984C\uFF0C\u800C\u5C07\u6240\u6709NP\u5B8C\u5168\u554F\u984C\u6B78\u7D04\u6210\u5206\u5718\u8986\u84CB\u554F\u984C\u3002\u6545\u5206\u5718\u8986\u84CB\u554F\u984C\u662FNP\u5B8C\u5168\u554F\u984C\u3002 \u76F8\u95DC\u7684\u554F\u984C\u5247\u662F\u8003\u616E\u662F\u5426\u5B58\u5728\u5206\u5718\u7684\u96C6\u5408\u80FD\u5305\u542B\u5716\u4E2D\u6240\u6709\u7684\u908A\uFF08edge\uFF09\u3002\u9019\u500B\u554F\u984C\u4E5F\u4E00\u6A23\u662FNP\u5B8C\u5168\u554F\u984C\u3002"@zh . . . "\u0417\u0430\u0434\u0430\u0447\u0430 \u043F\u0440\u043E \u043A\u043B\u0456\u043A\u043E\u0432\u0435 \u043F\u043E\u043A\u0440\u0438\u0442\u0442\u044F \u2014 \u043E\u0431\u0447\u0438\u0441\u043B\u044E\u0432\u0430\u043B\u044C\u043D\u0430 \u0437\u0430\u0434\u0430\u0447\u0430, \u044F\u043A\u0430 \u043F\u043E\u043B\u044F\u0433\u0430\u0454 \u0443 \u0432\u0438\u0437\u043D\u0430\u0447\u0435\u043D\u043D\u0456 \u043C\u043E\u0436\u043B\u0438\u0432\u043E\u0441\u0442\u0456 \u0440\u043E\u0437\u0431\u0438\u0442\u0438 \u0432\u0435\u0440\u0448\u0438\u043D\u0438 \u0433\u0440\u0430\u0444\u0443 \u043D\u0430 \u043A\u043B\u0456\u043A. \u0404 NP-\u043F\u043E\u0432\u043D\u043E\u044E; \u0432\u0445\u043E\u0434\u0438\u0442\u044C \u0434\u043E \u0447\u0438\u0441\u043B\u0430 21 NP-\u043F\u043E\u0432\u043D\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 \u041A\u0430\u0440\u043F\u0430. \u042F\u043A\u0449\u043E \u0434\u0430\u043D\u043E \u0440\u043E\u0437\u0431\u0438\u0442\u0442\u044F \u0432\u0435\u0440\u0448\u0438\u043D \u043D\u0430 \u043C\u043D\u043E\u0436\u0438\u043D, \u0442\u043E \u043C\u043E\u0436\u043D\u0430 \u0437\u0430 \u043F\u043E\u043B\u0456\u043D\u043E\u043C\u0456\u0430\u043B\u044C\u043D\u0438\u0439 \u0447\u0430\u0441 \u0432\u0438\u0437\u043D\u0430\u0447\u0438\u0442\u0438, \u0449\u043E \u043A\u043E\u0436\u043D\u0430 \u043C\u043D\u043E\u0436\u0438\u043D\u0430 \u0443\u0442\u0432\u043E\u0440\u044E\u0454 \u043A\u043B\u0456\u043A\u0443 \u0442\u0430\u043A, \u0449\u043E \u0437\u0430\u0434\u0430\u0447\u0430 \u043D\u0430\u043B\u0435\u0436\u0438\u0442\u044C \u0434\u043E \u043A\u043B\u0430\u0441\u0443 NP. NP-\u043F\u043E\u0432\u043D\u043E\u0442\u0430 \u0437\u0430\u0434\u0430\u0447\u0456 \u043F\u0440\u043E \u043A\u043B\u0456\u043A\u043E\u0432\u0435 \u043F\u043E\u043A\u0440\u0438\u0442\u0442\u044F \u0432\u0438\u043F\u043B\u0438\u0432\u0430\u0454 \u0437\u0456 \u0437\u0432\u0435\u0434\u0435\u043D\u043D\u044F \u0457\u0457 \u0434\u043E \u0437\u0430\u0434\u0430\u0447\u0456 \u0440\u043E\u0437\u0444\u0430\u0440\u0431\u043E\u0432\u0443\u0432\u0430\u043D\u043D\u044F \u0433\u0440\u0430\u0444\u0443: \u0440\u043E\u0437\u043A\u043B\u0430\u0434\u0430\u043D\u043D\u044F \u0433\u0440\u0430\u0444\u0443 \u043D\u0430 \u043A\u043B\u0456\u043A \u0432\u0456\u0434\u043F\u043E\u0432\u0456\u0434\u0430\u0454 \u0437\u043D\u0430\u0445\u043E\u0434\u0436\u0435\u043D\u043D\u044E \u0440\u043E\u0437\u043A\u043B\u0430\u0434\u0443 \u0432\u0435\u0440\u0448\u0438\u043D \u0434\u043E\u043F\u043E\u0432\u043D\u0435\u043D\u043D\u044F \u043D\u0430 \u043D\u0435\u0437\u0430\u043B\u0435\u0436\u043D\u0438\u0445 \u043C\u043D\u043E\u0436\u0438\u043D (\u043A\u043E\u0436\u043D\u0456\u0439 \u0456\u0437 \u0446\u0438\u0445 \u043C\u043D\u043E\u0436\u0438\u043D \u043C\u043E\u0436\u043D\u0430 \u043F\u0440\u0438\u0437\u043D\u0430\u0447\u0438\u0442\u0438 \u043E\u0434\u0438\u043D \u043A\u043E\u043B\u0456\u0440, \u0449\u043E \u0434\u0430\u0441\u0442\u044C -\u0440\u043E\u0437\u0444\u0430\u0440\u0431\u0443\u0432\u0430\u043D\u043D\u044F)."@uk . . . . "\u6700\u5C0F\u30AF\u30EA\u30FC\u30AF\u88AB\u8986\u554F\u984C"@ja . . . "Nella teoria della complessit\u00E0 computazionale, trovare una copertura delle cricche minima \u00E8 un problema NP-completo di teoria dei grafi. Il probalma era uno dei 21 problemi originali di Richard Karp che erano stati dimostrati NP-completi nel suo saggio del 1972 Riducibilit\u00E0 tra problemi combinatori (Reducibility among Combinatorial Problems). Il problema correlato della considera gli insiemi delle cricche che comprendono tutti gli spigoli di un dato grafo. Anch'esso \u00E8 NP-completo."@it . . . . . . "\u0417\u0430\u0434\u0430\u0447\u0430 \u043F\u0440\u043E \u043A\u043B\u0456\u043A\u043E\u0432\u0435 \u043F\u043E\u043A\u0440\u0438\u0442\u0442\u044F \u2014 \u043E\u0431\u0447\u0438\u0441\u043B\u044E\u0432\u0430\u043B\u044C\u043D\u0430 \u0437\u0430\u0434\u0430\u0447\u0430, \u044F\u043A\u0430 \u043F\u043E\u043B\u044F\u0433\u0430\u0454 \u0443 \u0432\u0438\u0437\u043D\u0430\u0447\u0435\u043D\u043D\u0456 \u043C\u043E\u0436\u043B\u0438\u0432\u043E\u0441\u0442\u0456 \u0440\u043E\u0437\u0431\u0438\u0442\u0438 \u0432\u0435\u0440\u0448\u0438\u043D\u0438 \u0433\u0440\u0430\u0444\u0443 \u043D\u0430 \u043A\u043B\u0456\u043A. \u0404 NP-\u043F\u043E\u0432\u043D\u043E\u044E; \u0432\u0445\u043E\u0434\u0438\u0442\u044C \u0434\u043E \u0447\u0438\u0441\u043B\u0430 21 NP-\u043F\u043E\u0432\u043D\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 \u041A\u0430\u0440\u043F\u0430. \u042F\u043A\u0449\u043E \u0434\u0430\u043D\u043E \u0440\u043E\u0437\u0431\u0438\u0442\u0442\u044F \u0432\u0435\u0440\u0448\u0438\u043D \u043D\u0430 \u043C\u043D\u043E\u0436\u0438\u043D, \u0442\u043E \u043C\u043E\u0436\u043D\u0430 \u0437\u0430 \u043F\u043E\u043B\u0456\u043D\u043E\u043C\u0456\u0430\u043B\u044C\u043D\u0438\u0439 \u0447\u0430\u0441 \u0432\u0438\u0437\u043D\u0430\u0447\u0438\u0442\u0438, \u0449\u043E \u043A\u043E\u0436\u043D\u0430 \u043C\u043D\u043E\u0436\u0438\u043D\u0430 \u0443\u0442\u0432\u043E\u0440\u044E\u0454 \u043A\u043B\u0456\u043A\u0443 \u0442\u0430\u043A, \u0449\u043E \u0437\u0430\u0434\u0430\u0447\u0430 \u043D\u0430\u043B\u0435\u0436\u0438\u0442\u044C \u0434\u043E \u043A\u043B\u0430\u0441\u0443 NP. NP-\u043F\u043E\u0432\u043D\u043E\u0442\u0430 \u0437\u0430\u0434\u0430\u0447\u0456 \u043F\u0440\u043E \u043A\u043B\u0456\u043A\u043E\u0432\u0435 \u043F\u043E\u043A\u0440\u0438\u0442\u0442\u044F \u0432\u0438\u043F\u043B\u0438\u0432\u0430\u0454 \u0437\u0456 \u0437\u0432\u0435\u0434\u0435\u043D\u043D\u044F \u0457\u0457 \u0434\u043E \u0437\u0430\u0434\u0430\u0447\u0456 \u0440\u043E\u0437\u0444\u0430\u0440\u0431\u043E\u0432\u0443\u0432\u0430\u043D\u043D\u044F \u0433\u0440\u0430\u0444\u0443: \u0440\u043E\u0437\u043A\u043B\u0430\u0434\u0430\u043D\u043D\u044F \u0433\u0440\u0430\u0444\u0443 \u043D\u0430 \u043A\u043B\u0456\u043A \u0432\u0456\u0434\u043F\u043E\u0432\u0456\u0434\u0430\u0454 \u0437\u043D\u0430\u0445\u043E\u0434\u0436\u0435\u043D\u043D\u044E \u0440\u043E\u0437\u043A\u043B\u0430\u0434\u0443 \u0432\u0435\u0440\u0448\u0438\u043D \u0434\u043E\u043F\u043E\u0432\u043D\u0435\u043D\u043D\u044F \u043D\u0430 \u043D\u0435\u0437\u0430\u043B\u0435\u0436\u043D\u0438\u0445 \u043C\u043D\u043E\u0436\u0438\u043D (\u043A\u043E\u0436\u043D\u0456\u0439 \u0456\u0437 \u0446\u0438\u0445 \u043C\u043D\u043E\u0436\u0438\u043D \u043C\u043E\u0436\u043D\u0430 \u043F\u0440\u0438\u0437\u043D\u0430\u0447\u0438\u0442\u0438 \u043E\u0434\u0438\u043D \u043A\u043E\u043B\u0456\u0440, \u0449\u043E \u0434\u0430\u0441\u0442\u044C -\u0440\u043E\u0437\u0444\u0430\u0440\u0431\u0443\u0432\u0430\u043D\u043D\u044F). \u041D\u0430\u0439\u043C\u0435\u043D\u0448\u0438\u0439 \u0440\u043E\u0437\u043C\u0456\u0440 \u043A\u043B\u0456\u043A\u043E\u0432\u043E\u0433\u043E \u043F\u043E\u043A\u0440\u0438\u0442\u0442\u044F \u0433\u0440\u0430\u0444\u0443 \u2014 \u043D\u0430\u0439\u043C\u0435\u043D\u0448\u0435 \u0447\u0438\u0441\u043B\u043E , \u0434\u043B\u044F \u044F\u043A\u043E\u0433\u043E \u043A\u043B\u0456\u043A\u043E\u0432\u0435 \u043F\u043E\u043A\u0440\u0438\u0442\u0442\u044F \u0456\u0441\u043D\u0443\u0454. \u041F\u043E\u0432'\u044F\u0437\u0430\u043D\u0430 \u0437\u0430\u0434\u0430\u0447\u0430 \u0437\u043D\u0430\u0445\u043E\u0434\u0436\u0435\u043D\u043D\u044F \u0447\u0438\u0441\u043B\u0430 \u043F\u0435\u0440\u0435\u0442\u0438\u043D\u0456\u0432 \u0440\u043E\u0437\u0433\u043B\u044F\u0434\u0430\u0454 \u043C\u043D\u043E\u0436\u0438\u043D\u0438 \u043A\u043B\u0456\u043A, \u0449\u043E \u0432\u043A\u043B\u044E\u0447\u0430\u044E\u0442\u044C \u0443\u0441\u0456 \u0440\u0435\u0431\u0440\u0430 \u0434\u0430\u043D\u043E\u0433\u043E \u0433\u0440\u0430\u0444\u0443; \u0446\u044F \u0437\u0430\u0434\u0430\u0447\u0430 \u0442\u0430\u043A\u043E\u0436 NP-\u043F\u043E\u0432\u043D\u0430."@uk . . . "\u0417\u0430\u0434\u0430\u0447\u0430 \u043E \u043A\u043B\u0438\u043A\u043E\u0432\u043E\u043C \u043F\u043E\u043A\u0440\u044B\u0442\u0438\u0438"@ru . . . . . . "Em complexidade computacional, encontrar uma cobertura de clique min\u00EDma \u00E9 um problema NP-completo relacionado \u00E0 Teoria dos grafos. Este problema foi um dos 21 problemas originais de Karp mostrados serem NP-completos em seu artigo de 1972 \"Reducibility Among Combinatorial Problems\" (Redutibilidade entre problemas combinat\u00F3rios). O Problema da cobertura de clique (tamb\u00E9m chamado as vezes de parti\u00E7\u00E3o em cliques) \u00E9 o problema de se determinar se os v\u00E9rtices de um grafo podem ser particionados em k . Dada uma parti\u00E7\u00E3o dos vertices em k conjuntos, pode ser verificado em [tempo polinomial] que cada conjunto forma um clique, ent\u00E3o o problema est\u00E1 em NP. A NP-completude de uma cobertura clique segue de uma redu\u00E7\u00E3o da k-Colorabilidade de um grafo. Para ver tal redu\u00E7\u00E3o, primeiros transformamos uma inst\u00E2ncia G de um k-colorabilidade Grafo em seu Grafo complementar G'. Uma parti\u00E7\u00E3o de G' em k cliques ent\u00E3o corresponde a encontrar uma parti\u00E7\u00E3o dos vertices de G em k ; a cada um desses conjuntos pode ent\u00E3o ser atribu\u00EDda uma cor para ser produzida uma k-colora\u00E7\u00E3o. O problema relacionado considera conjuntos de cliques que incluem todas as arestas de um dado caminho. Ele tamb\u00E9m \u00E9 NP-completo."@pt . . . . "\u8A08\u7B97\u91CF\u7406\u8AD6\u306B\u304A\u3044\u3066\u3001\u6700\u5C0F\u306E\u30AF\u30EA\u30FC\u30AF\u88AB\u8986\uFF08\u30AF\u30EA\u30FC\u30AF\u3072\u3075\u304F\u3001\u82F1: clique cover\uFF09\u3092\u6C42\u3081\u308B\u3053\u3068\u306F\u3001\u30B0\u30E9\u30D5\u7406\u8AD6\u7684NP\u5B8C\u5168\u554F\u984C\u3067\u3042\u308B\u3002\u30AF\u30EA\u30FC\u30AF\u88AB\u8986\u554F\u984C\u306F\u306E1\u3064\u3067\u3001\u305D\u306ENP\u5B8C\u5168\u6027\u306F1972\u5E74\u306E\u8AD6\u6587 \"Reducibility Among Combinatorial Problems\"\uFF08\u300C\u7D44\u5408\u305B\u8AD6\u7684\u554F\u984C\u9593\u306E\u9084\u5143\u53EF\u80FD\u6027\u300D\uFF09\u306B\u793A\u3055\u308C\u3066\u3044\u308B\u3002 \u30AF\u30EA\u30FC\u30AF\u88AB\u8986\u554F\u984C\uFF08\u30AF\u30EA\u30FC\u30AF\u5206\u5272\u554F\u984C\u3068\u547C\u3076\u3053\u3068\u3082\u3042\u308B\uFF09\u3068\u306F\u3001\u4E0E\u3048\u3089\u308C\u305F\u30B0\u30E9\u30D5\u306E\u9802\u70B9\u96C6\u5408\u3092 k-\u500B\u306E\u30AF\u30EA\u30FC\u30AF\u3078\u5206\u5272\u3067\u304D\u308B\u304B\u3092\u6C7A\u5B9A\u3059\u308B\u554F\u984C\u3067\u3042\u308B\u3002\u9802\u70B9\u96C6\u5408\u306E k-\u500B\u306E\u96C6\u5408\u3078\u306E\u5206\u5272\u304C\u4E0E\u3048\u3089\u308C\u305F\u3068\u304D\u3001\u305D\u306E\u5404\u96C6\u5408\u304C\u30AF\u30EA\u30FC\u30AF\u3092\u6210\u3059\u304B\u306F\u591A\u9805\u5F0F\u6642\u9593\u3067\u5224\u5B9A\u3059\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u304B\u3089\u3001\u30AF\u30EA\u30FC\u30AF\u88AB\u8986\u554F\u984C\u306FNP\u306B\u5C5E\u3059\u308B\u3002\u305D\u306ENP\u5B8C\u5168\u6027\u306F\u30B0\u30E9\u30D5\u306E k-\u5F69\u8272\u53EF\u80FD\u6027\u304B\u3089\u306E\u5E30\u7740\u3067\u3042\u308B\u3002\u3053\u308C\u3092\u898B\u308B\u306B\u306F\u3001\u307E\u305A\u30B0\u30E9\u30D5 G \u306E k-\u5F69\u8272\u53EF\u80FD\u6027\u3092\u305D\u306E\u88DC\u30B0\u30E9\u30D5 G\u2032 \u306B\u95A2\u3059\u308B\u4E8B\u5B9F\u306B\u7FFB\u8A33\u3059\u308C\u3070\u3088\u3044\u3002\u3053\u306E\u3068\u304D G \u306E k-\u500B\u306E\u30AF\u30EA\u30FC\u30AF\u3078\u306E\u5206\u5272\u306F G\u2032 \u306E k-\u500B\u306E\u72EC\u7ACB\u96C6\u5408\u3078\u306E\u5206\u5272\u3092\u6C42\u3081\u308B\u3053\u3068\u306B\u5BFE\u5FDC\u3059\u308B\uFF08\u5404\u96C6\u5408\u306B\u305D\u308C\u305E\u308C\u5225\u306E1\u3064\u306E\u8272\u3092\u5857\u308B\u3053\u3068\u3067 k-\u5F69\u8272\u304C\u3067\u304D\u305F\u3053\u3068\u306B\u306A\u308B\uFF09\u3002 \u3053\u306E\u554F\u984C\u3068\u95A2\u9023\u3057\u3066\u3001\u554F\u984C\u306F\u4E0E\u3048\u3089\u308C\u305F\u30B0\u30E9\u30D5\u306E\u8FBA\u3092\u3059\u3079\u3066\u542B\u3080\u3088\u3046\u306A\u30AF\u30EA\u30FC\u30AF\u306E\u96C6\u5408\u3092\u8003\u3048\u308B\u3082\u306E\u3067\u3001\u3053\u308C\u3082\u307E\u305FNP\u5B8C\u5168\u554F\u984C\u3067\u3042\u308B\u3002"@ja . . "Problema di copertura delle cricche"@it . . . "Nella teoria della complessit\u00E0 computazionale, trovare una copertura delle cricche minima \u00E8 un problema NP-completo di teoria dei grafi. Il probalma era uno dei 21 problemi originali di Richard Karp che erano stati dimostrati NP-completi nel suo saggio del 1972 Riducibilit\u00E0 tra problemi combinatori (Reducibility among Combinatorial Problems). IL problema di copertura delle cricche (a volte chiamato anche partizione in cricche) \u00E8 il problema di determinare se i vertici di un grafo possono essere ripartiti in k cricche. Data una partizione dei vertici in k insiemi, si pu\u00F2 verificare in tempo polinomiale che ciascun insieme forma una cricca, per cui il problema \u00E8 in NP. La NP-completezza della copertura delle cricche consegue mediante riduzione dalla k-colorabilit\u00E0 del grafo. Per vedere questo, si trasformi dapprima un'istanza G di k-colorabilit\u00E0 del grafo nel suo grafo complemento G'. Una partizione di G' in k cricche corrisponde allora a trovare una partizione dei vertici di G in k insiemi indipendenti; a ognuno di questi insiemi si pu\u00F2 allora assegnare un colore per creare una k-colorazione. Il problema correlato della considera gli insiemi delle cricche che comprendono tutti gli spigoli di un dato grafo. Anch'esso \u00E8 NP-completo."@it . . . . . . "1096498928"^^ . "Em complexidade computacional, encontrar uma cobertura de clique min\u00EDma \u00E9 um problema NP-completo relacionado \u00E0 Teoria dos grafos. Este problema foi um dos 21 problemas originais de Karp mostrados serem NP-completos em seu artigo de 1972 \"Reducibility Among Combinatorial Problems\" (Redutibilidade entre problemas combinat\u00F3rios). O problema relacionado considera conjuntos de cliques que incluem todas as arestas de um dado caminho. Ele tamb\u00E9m \u00E9 NP-completo."@pt . . . "\u5728\u8A08\u7B97\u8907\u96DC\u5EA6\u7406\u8AD6\u5167\uFF0C\u627E\u4E00\u500B\u6700\u5C0F\u7684\u5206\u5718\u8986\u84CB\uFF08clique cover\uFF09\u662F\u4E00\u500B\u5716\u8AD6\u7684NP\u5B8C\u5168\u554F\u984C\u3002\u9019\u554F\u984C\u5C6C\u65BC\u5361\u666E\u7684\u4E8C\u5341\u4E00\u500BNP-\u5B8C\u5168\u554F\u984C\u4E4B\u4E00\uFF0C\u7531\u5361\u666E\u57281972\u5E74\u7684\u8AD6\u6587\"Reducibility Among Combinatorial Problems\"\u8B49\u660E\u70BANP\u5B8C\u5168\u3002 \u5206\u5718\u8986\u84CB\u554F\u984C\uFF08\u6709\u6642\u53EB\u505A\u5206\u6210\u5206\u5718\uFF0Cpartition into cliques\uFF09\u662F\u554F\u4E00\u500B\u5716\u88E1\u9762\u7684\u6240\u6709\u9EDE\u53EF\u5426\u5206\u6210k\u500B\u3002\u4E00\u65E6\u7D66\u5B9A\u4E86\u9019\u500B\u5716\u8A72\u600E\u9EBC\u5206\u6210k\u500B\u5206\u5718\uFF0C\u6211\u5011\u53EF\u4EE5\u5728\u591A\u9805\u5F0F\u6642\u9593\u88E1\u9762\u6AA2\u8B49\u9019\u500B\u7B54\u6848\u662F\u5426\u6B63\u78BA\uFF0C\u56E0\u6B64\u6211\u5011\u53EF\u4EE5\u77E5\u9053\u9019\u500B\u554F\u984C\u5C6C\u65BCNP\u3002 \u5206\u5718\u8986\u84CB\u554F\u984C\u662FNP\u5B8C\u5168\u9019\u4EF6\u4E8B\u60C5\uFF0C\u53EF\u4EE5\u85C9\u7531\u5C07\u6B64\u554F\u984C\u5F9Ek-\u5716\u8457\u8272\u554F\u984C\uFF08GRAPH k-COLOURABILITY\uFF09\u6B78\u7D04\u51FA\u4F86\u800C\u5F97\u8B49\u3002\u8981\u63A8\u51FA\u9019\u500B\u7D50\u679C\uFF0C\u9996\u5148\u6211\u5011\u5C07\u4E00\u500Bk-\u5716\u8457\u8272\u554F\u984C\u7684\u8F38\u5165\u5716G\u8F49\u6210\u5176\u88DC\u5716G'\u3002\u90A3\u9EBC\uFF0C\u6C42\u51FAG' \u600E\u9EBC\u5206\u51FAk\u500B\u5206\u5718\u9019\u554F\u984C\u5C31\u7B49\u540C\u65BC\u6C42\u51FAG\u600E\u9EBC\u5206\u51FAk\u500B\u7368\u7ACB\u96C6\uFF1B\u6211\u5011\u80FD\u5C07\u6BCF\u500B\u7368\u7ACB\u96C6\u8A2D\u7ACB\u4E00\u500B\u984F\u8272\u4F86\u5F97\u5230k\u500B\u984F\u8272\uFF0C\u4E26\u4E14\u4FDD\u8B49G\u5167\u6240\u6709\u76F8\u540C\u984F\u8272\u7684\u9EDE\u4E0D\u6703\u4E92\u76F8\u9023\u63A5\u3002\u56E0\u6B64\uFF0C\u89E3\u51FAG' \u7684\u5206\u5718\u554F\u984C\uFF0C\u5373\u662F\u89E3\u51FAG\u7684\u8457\u8272\u554F\u984C\u3002\u56E0\u70BA\u6211\u5011\u5DF2\u77E5k-\u8457\u8272\u554F\u984C\u662FNP\u5B8C\u5168\u554F\u984C\uFF0C\u6240\u4EE5\u6211\u5011\u80FD\u85C9\u7531\u5C07\u6240\u6709NP\u7684\u554F\u984C\u5148\u6B78\u7D04\u70BAk-\u8457\u8272\u554F\u984C\uFF0C\u518D\u6B78\u7D04\u70BA\u5206\u5718\u8986\u84CB\u554F\u984C\uFF0C\u800C\u5C07\u6240\u6709NP\u5B8C\u5168\u554F\u984C\u6B78\u7D04\u6210\u5206\u5718\u8986\u84CB\u554F\u984C\u3002\u6545\u5206\u5718\u8986\u84CB\u554F\u984C\u662FNP\u5B8C\u5168\u554F\u984C\u3002 \u76F8\u95DC\u7684\u554F\u984C\u5247\u662F\u8003\u616E\u662F\u5426\u5B58\u5728\u5206\u5718\u7684\u96C6\u5408\u80FD\u5305\u542B\u5716\u4E2D\u6240\u6709\u7684\u908A\uFF08edge\uFF09\u3002\u9019\u500B\u554F\u984C\u4E5F\u4E00\u6A23\u662FNP\u5B8C\u5168\u554F\u984C\u3002"@zh . . . . . . . . . "\u0417\u0430\u0434\u0430\u0447\u0430 \u043E \u043A\u043B\u0438\u043A\u043E\u0432\u043E\u043C \u043F\u043E\u043A\u0440\u044B\u0442\u0438\u0438 \u2014 \u0432\u044B\u0447\u0438\u0441\u043B\u0438\u0442\u0435\u043B\u044C\u043D\u0430\u044F \u0437\u0430\u0434\u0430\u0447\u0430, \u0437\u0430\u043A\u043B\u044E\u0447\u0430\u044E\u0449\u0430\u044F\u0441\u044F \u0432 \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0435\u043D\u0438\u0438 \u0432\u043E\u0437\u043C\u043E\u0436\u043D\u043E\u0441\u0442\u0438 \u0440\u0430\u0437\u0431\u0438\u0442\u044C \u0432\u0435\u0440\u0448\u0438\u043D\u044B \u0433\u0440\u0430\u0444\u0430 \u043D\u0430 \u043A\u043B\u0438\u043A. \u042F\u0432\u043B\u044F\u0435\u0442\u0441\u044F NP-\u043F\u043E\u043B\u043D\u043E\u0439; \u0432\u0445\u043E\u0434\u0438\u0442 \u0432 \u0441\u043F\u0438\u0441\u043E\u043A \u0438\u0437 21 NP-\u043F\u043E\u043B\u043D\u044B\u0445 \u0437\u0430\u0434\u0430\u0447 \u041A\u0430\u0440\u043F\u0430. \u0415\u0441\u043B\u0438 \u0434\u0430\u043D\u043E \u0440\u0430\u0437\u0431\u0438\u0435\u043D\u0438\u0435 \u0432\u0435\u0440\u0448\u0438\u043D \u043D\u0430 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432, \u0442\u043E \u043C\u043E\u0436\u043D\u043E \u0437\u0430 \u043F\u043E\u043B\u0438\u043D\u043E\u043C\u0438\u0430\u043B\u044C\u043D\u043E\u0435 \u0432\u0440\u0435\u043C\u044F \u043E\u043F\u0440\u0435\u0434\u0435\u043B\u0438\u0442\u044C, \u0447\u0442\u043E \u043A\u0430\u0436\u0434\u043E\u0435 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E \u043E\u0431\u0440\u0430\u0437\u0443\u0435\u0442 \u043A\u043B\u0438\u043A\u0443 \u0442\u0430\u043A, \u0447\u0442\u043E \u0437\u0430\u0434\u0430\u0447\u0430 \u043F\u0440\u0438\u043D\u0430\u0434\u043B\u0435\u0436\u0438\u0442 \u043A\u043B\u0430\u0441\u0441\u0443 NP. NP-\u043F\u043E\u043B\u043D\u043E\u0442\u0430 \u0437\u0430\u0434\u0430\u0447\u0438 \u043E \u043A\u043B\u0438\u043A\u043E\u0432\u043E\u043C \u043F\u043E\u043A\u0440\u044B\u0442\u0438\u0438 \u0441\u043B\u0435\u0434\u0443\u0435\u0442 \u0438\u0437 \u0441\u0432\u0435\u0434\u0435\u043D\u0438\u044F \u0435\u0451 \u043A \u0437\u0430\u0434\u0430\u0447\u0435 \u0440\u0430\u0441\u043A\u0440\u0430\u0441\u043A\u0438 \u0433\u0440\u0430\u0444\u0430: \u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u0435 \u0433\u0440\u0430\u0444\u0430 \u043D\u0430 \u043A\u043B\u0438\u043A \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u043D\u0430\u0445\u043E\u0436\u0434\u0435\u043D\u0438\u044E \u0440\u0430\u0437\u043B\u043E\u0436\u0435\u043D\u0438\u044F \u0432\u0435\u0440\u0448\u0438\u043D \u0434\u043E\u043F\u043E\u043B\u043D\u0435\u043D\u0438\u044F \u043D\u0430 \u043D\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043C\u044B\u0445 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432 (\u043A\u0430\u0436\u0434\u043E\u043C\u0443 \u0438\u0437 \u044D\u0442\u0438\u0445 \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432 \u043C\u043E\u0436\u043D\u043E \u043D\u0430\u0437\u043D\u0430\u0447\u0438\u0442\u044C \u043E\u0434\u0438\u043D \u0446\u0432\u0435\u0442, \u0447\u0442\u043E \u0434\u0430\u0441\u0442 -\u0440\u0430\u0441\u043A\u0440\u0430\u0441\u043A\u0443)."@ru . "Clique cover"@en .

  NODES