Maximum colorful independent sets in vertex-colored graphs

Q2 Mathematics

Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI:10.1016/j.endm.2018.06.043

Yannis Manoussakis, Hong Phong Pham

引用次数: 1

Abstract

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.

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顶点彩色图形中彩色独立集的最大值

本文研究了在顶点彩色图中寻找最大彩色独立集的问题。具体来说，给定一个带有彩色顶点的图，我们希望找到一个包含最大数量颜色的独立集。在这里，我们的目的是对这个问题的复杂性给出一个二分的概述。我们首先证明了这个问题是np困难的，即使在一些最大独立集问题很容易的情况下，比如图和P5-free图。接下来，我们为聚类图和树提供多项式时间算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

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