On the minimum and maximum selective graph coloring problems in some graph classes

被引:6
|
作者
Demange, Marc [1 ]
Ekim, Tinaz [2 ]
Ries, Bernard [3 ]
机构
[1] RMIT Univ, Melbourne, Vic, Australia
[2] Bogazici Univ, Istanbul, Turkey
[3] Univ Fribourg, DIUF, CH-1700 Fribourg, Switzerland
关键词
Complexity; Approximation; Graph classes; UNIT DISK GRAPHS; COMPLEXITY;
D O I
10.1016/j.dam.2015.10.005
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Given a graph together with a partition of its vertex set, the minimum selective coloring problem consists of selecting one vertex per partition set such that the chromatic number of the subgraph induced by the selected vertices is minimum. The contribution of this paper is twofold. First, we investigate the complexity status of the minimum selective coloring problem in some specific graph classes motivated by some models described in Demange et al. (2015). Second, we introduce a new problem that corresponds to the worst situation in the minimum selective coloring; the maximum selective coloring problem aims to select one vertex per partition set such that the chromatic number of the subgraph induced by the selected vertices is maximum. We motivate this problem by different models and give some first results concerning its complexity. (C) 2015 Elsevier B.V. All rights reserved.
引用
收藏
页码:77 / 89
页数:13
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