{"title":"关于参数化路径和无弦路径问题","authors":"Yijia Chen, J. Flum","doi":"10.1109/CCC.2007.21","DOIUrl":null,"url":null,"abstract":"We study the parameterized complexity of various path (and cycle) problems, the parameter being the length of the path. For example, we show that the problem of the existence of a maximal path of length k in a graph G is fixed-parameter tractable, while its counting version is #W[1]- complete. The corresponding problems for chordless (or induced) paths are W[2]-complete and #W[2]-complete respectively. With the tools developed in this paper we derive the NP-completeness of a related classical problem, thereby solving a problem due to Hedetniemi.","PeriodicalId":175854,"journal":{"name":"Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"43","resultStr":"{\"title\":\"On Parameterized Path and Chordless Path Problems\",\"authors\":\"Yijia Chen, J. Flum\",\"doi\":\"10.1109/CCC.2007.21\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the parameterized complexity of various path (and cycle) problems, the parameter being the length of the path. For example, we show that the problem of the existence of a maximal path of length k in a graph G is fixed-parameter tractable, while its counting version is #W[1]- complete. The corresponding problems for chordless (or induced) paths are W[2]-complete and #W[2]-complete respectively. With the tools developed in this paper we derive the NP-completeness of a related classical problem, thereby solving a problem due to Hedetniemi.\",\"PeriodicalId\":175854,\"journal\":{\"name\":\"Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-06-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"43\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CCC.2007.21\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CCC.2007.21","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We study the parameterized complexity of various path (and cycle) problems, the parameter being the length of the path. For example, we show that the problem of the existence of a maximal path of length k in a graph G is fixed-parameter tractable, while its counting version is #W[1]- complete. The corresponding problems for chordless (or induced) paths are W[2]-complete and #W[2]-complete respectively. With the tools developed in this paper we derive the NP-completeness of a related classical problem, thereby solving a problem due to Hedetniemi.
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