Approximation algorithms for clique-transversal sets and clique-independent sets in cubic graphs

Authors:
Zuosong Liang;Erfang Shan
Affiliations:
Department of Mathematics, Shanghai University, Shanghai 200444, China;Department of Mathematics, Shanghai University, Shanghai 200444, China
Venue:
Information Processing Letters
Year:
2011

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Abstract

A clique-transversal set S of a graph G is a subset of vertices intersecting all the cliques of G, where a clique is a complete subgraph maximal under inclusion and having at least two vertices. A clique-independent set of the graph G is a set of pairwise disjoint cliques of G. The clique-transversal number@t"C(G) of G is the cardinality of the smallest clique-transversal set in G and the clique-independence number@a"C(G) of G is the cardinality of the largest clique-independent set in G. This paper proves that determining @t"C(G) and @a"C(G) is NP-complete for a cubic planar graph G of girth 3. Further we propose two approximation algorithms for determining @t"C(G) and @a"C(G) in a cubic graph G.