{"title":"最大子图问题的复杂性","authors":"John M. Lewis","doi":"10.1145/800133.804356","DOIUrl":null,"url":null,"abstract":"For a fixed graph property, the Maximum Subgraph Recognition Problem for the property is: Given a graph G and integer k, does G have a subgraph induced by k vertices which satisfies the property. This paper studies the complexity of this problem for various properties. The principal result is that if the property is any one of a wide class of monotone properties, the Maximum Subgraph Problem is NP-hard. This suggests a promising direction of inquiry into the P = ?NP question.","PeriodicalId":313820,"journal":{"name":"Proceedings of the tenth annual ACM symposium on Theory of computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1978-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"35","resultStr":"{\"title\":\"On the complexity of the Maximum Subgraph Problem\",\"authors\":\"John M. Lewis\",\"doi\":\"10.1145/800133.804356\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a fixed graph property, the Maximum Subgraph Recognition Problem for the property is: Given a graph G and integer k, does G have a subgraph induced by k vertices which satisfies the property. This paper studies the complexity of this problem for various properties. The principal result is that if the property is any one of a wide class of monotone properties, the Maximum Subgraph Problem is NP-hard. This suggests a promising direction of inquiry into the P = ?NP question.\",\"PeriodicalId\":313820,\"journal\":{\"name\":\"Proceedings of the tenth annual ACM symposium on Theory of computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1978-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"35\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the tenth annual ACM symposium on Theory of computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/800133.804356\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the tenth annual ACM symposium on Theory of computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/800133.804356","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
For a fixed graph property, the Maximum Subgraph Recognition Problem for the property is: Given a graph G and integer k, does G have a subgraph induced by k vertices which satisfies the property. This paper studies the complexity of this problem for various properties. The principal result is that if the property is any one of a wide class of monotone properties, the Maximum Subgraph Problem is NP-hard. This suggests a promising direction of inquiry into the P = ?NP question.