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2016

Hierarchical complexity of 2-clique-colouring weakly chordal graphs and perfect graphs having cliques of size at least 3

3 years 6 months ago
Hierarchical complexity of 2-clique-colouring weakly chordal graphs and perfect graphs having cliques of size at least 3
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. D´efossez proved that the 2-cliquecolouring of perfect graphs is a ΣP 2 -complete problem [J. Graph Theory 62 (2009) 139–156]. We strengthen this result by showing that it is still ΣP 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 ΣP 2 -complete, NP-complete, and P. We solve an open problem posed by Kratochv´ıl 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 ΣP 2 -complete problem. We then determine a hierarchy of nested subclasses of perfect graphs with all cliques having size at least 3 whereby each...
Hélio B. Macêdo Filho, Raphael C. S.
Added 10 Apr 2016
Updated 10 Apr 2016
Type Journal
Year 2016
Where TCS
Authors Hélio B. Macêdo Filho, Raphael C. S. Machado, Celina M. Herrera de Figueiredo
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