{"title":"顶点彩色图形中彩色独立集的最大值","authors":"Yannis Manoussakis, Hong Phong Pham","doi":"10.1016/j.endm.2018.06.043","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we study the problem of finding a maximum colorful independent set in vertex-colored graphs. Specifically, given a graph with colored vertices, we wish to find an independent set containing the maximum number of colors. Here we aim to give a dichotomy overview on the complexity of this problem. We first show that the problem is NP-hard even for some cases where the maximum independent set problem is easy, such as cographs and <em>P</em><sub>5</sub>-free graphs. Next, we provide polynomial-time algorithms for cluster graphs and trees.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.043","citationCount":"1","resultStr":"{\"title\":\"Maximum colorful independent sets in vertex-colored graphs\",\"authors\":\"Yannis Manoussakis, Hong Phong Pham\",\"doi\":\"10.1016/j.endm.2018.06.043\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper we study the problem of finding a maximum colorful independent set in vertex-colored graphs. Specifically, given a graph with colored vertices, we wish to find an independent set containing the maximum number of colors. Here we aim to give a dichotomy overview on the complexity of this problem. We first show that the problem is NP-hard even for some cases where the maximum independent set problem is easy, such as cographs and <em>P</em><sub>5</sub>-free graphs. Next, we provide polynomial-time algorithms for cluster graphs and trees.</p></div>\",\"PeriodicalId\":35408,\"journal\":{\"name\":\"Electronic Notes in Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.043\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Notes in Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1571065318301343\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Notes in Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1571065318301343","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
Maximum colorful independent sets in vertex-colored graphs
In this paper we study the problem of finding a maximum colorful independent set in vertex-colored graphs. Specifically, given a graph with colored vertices, we wish to find an independent set containing the maximum number of colors. Here we aim to give a dichotomy overview on the complexity of this problem. We first show that the problem is NP-hard even for some cases where the maximum independent set problem is easy, such as cographs and P5-free graphs. Next, we provide polynomial-time algorithms for cluster graphs and trees.
期刊介绍：
Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.
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