On the complexity of bicoloring clique hypergraphs of graphs

Authors:
Jan Kratochvíl;Zsolt Tuza
Affiliations:
Department of Applied Mathematics and Institute of Theoretical Computer Science, Charles University, Malostranské nám. 25, 118 00 Prague, Czech Republic;Computer and Automation Institute, Hungarian Academy of Sciences, H-1111 Budapest, Kende u. 13-17, Hungary
Venue:
Journal of Algorithms
Year:
2002

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Abstract

Given a graph G, its clique hypergraph C(G) has the same set of vertices as G and the hyperedges correspond to the (inclusionwise) maximal cliques of G. We consider the question of bicolorability of C(G), i.e., whether the vertices of G can be colored with two colors so that no maximal clique is monochromatic. Our two main results say that deciding the bicolorability of C(G) is NP-hard for perfect graphs (and even for those with clique number 3), but solvable in polynomial time for planar graphs.