Hierarchical Complexity of 2-Clique-Colouring Weakly Chordal Graphs and Perfect Graphs Having Cliques of Size at Least 3

被引：0
|
作者：
Macedo Filho, Helio B. [1 ]
Machado, Raphael C. S. [2 ]
Figueiredo, Celina M. H. [1 ]
机构：
[1] Univ Fed Rio de Janeiro, COPPE, BR-21941 Rio De Janeiro, Brazil
[2] Inmetro Inst Nacl Metrologia, Qualidade Tecnologia, Quantico, VA USA
来源：
LATIN 2014: THEORETICAL INFORMATICS | 2014年 / 8392卷
关键词：
(alpha; beta)-polar graphs; clique-colouring; hierarchical complexity; perfect graphs; weakly chordal graphs;
D O I：
暂无
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
A clique of a graph is a maximal set of vertices of size at least 2 that induces a complete graph. A k-clique-colouring of a graph is a colouring of the vertices with at most k colours such that no clique is monochromatic. Defossez proved that the 2-clique-colouring of perfect graphs is a Sigma(P)(2)-complete problem [J. Graph Theory 62 ( 2009) 139-156]. We strengthen this result by showing that it is still Sigma(P)(2)-complete for weakly chordal graphs. We then determine a hierarchy of nested subclasses of weakly chordal graphs whereby each graph class is in a distinct complexity class, namely Sigma(P)(2)-complete, NP-complete, and P. We solve an open problem posed by Kratochvil and Tuza to determine the complexity of 2-clique-colouring of perfect graphs with all cliques having size at least 3 [J. Algorithms 45 ( 2002), 40-54], proving that it is a Sigma(P)(2)-complete problem. We then determine a hierarchy of nested subclasses of perfect graphs with all cliques having size at least 3 whereby each graph class is in a distinct complexity class, namely Sigma(P)(2)-complete, NP-complete, and P.
引用
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页码：13 / 23
页数：11
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