{"title":"节点和边删除np完全问题","authors":"M. Yannakakis","doi":"10.1145/800133.804355","DOIUrl":null,"url":null,"abstract":"If &pgr; is a graph property, the general node(edge) deletion problem can be stated as follows: Find the minimum number of nodes(edges), whose deletion results in a subgraph satisfying property &pgr;. In this paper we show that if &pgr; belongs to a rather broad class of properties (the class of properties that are hereditary on induced subgraphs) then the node-deletion problem is NP-complete, and the same is true for several restrictions of it. For the same class of properties, requiring the remaining graph to be connected does not change the NP-complete status of the problem; moreover for a certain subclass, finding any \"reasonable\" approximation is also NP-complete. Edge-deletion problems seem to be less amenable to such generalizations. We show however that for several common properties (e.g. planar, outer-planar, line-graph, transitive digraph) the edge-deletion problem is NP-complete.","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":"487","resultStr":"{\"title\":\"Node-and edge-deletion NP-complete problems\",\"authors\":\"M. Yannakakis\",\"doi\":\"10.1145/800133.804355\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"If &pgr; is a graph property, the general node(edge) deletion problem can be stated as follows: Find the minimum number of nodes(edges), whose deletion results in a subgraph satisfying property &pgr;. In this paper we show that if &pgr; belongs to a rather broad class of properties (the class of properties that are hereditary on induced subgraphs) then the node-deletion problem is NP-complete, and the same is true for several restrictions of it. For the same class of properties, requiring the remaining graph to be connected does not change the NP-complete status of the problem; moreover for a certain subclass, finding any \\\"reasonable\\\" approximation is also NP-complete. Edge-deletion problems seem to be less amenable to such generalizations. We show however that for several common properties (e.g. planar, outer-planar, line-graph, transitive digraph) the edge-deletion problem is NP-complete.\",\"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\":\"487\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the tenth annual ACM symposium on Theory of computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/800133.804355\",\"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/10.1145/800133.804355","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
If &pgr; is a graph property, the general node(edge) deletion problem can be stated as follows: Find the minimum number of nodes(edges), whose deletion results in a subgraph satisfying property &pgr;. In this paper we show that if &pgr; belongs to a rather broad class of properties (the class of properties that are hereditary on induced subgraphs) then the node-deletion problem is NP-complete, and the same is true for several restrictions of it. For the same class of properties, requiring the remaining graph to be connected does not change the NP-complete status of the problem; moreover for a certain subclass, finding any "reasonable" approximation is also NP-complete. Edge-deletion problems seem to be less amenable to such generalizations. We show however that for several common properties (e.g. planar, outer-planar, line-graph, transitive digraph) the edge-deletion problem is NP-complete.