Algorithmic aspects of the generalized clique-transversal problem on chordal graphs

Abstract

Suppose G=(V,E) is a graph in which each maximal clique C-i is associated with an integer r(i), where 0 less than or equal to r(i) less than or equal to\C-i\. The generalized clique transversal problem is to determine the minimum cardinality of a subset D of V such that \D boolean AND C-i\greater than or equal to r(i) for every maximal clique C-i of G. The problem includes the clique-transversal problem, the i,1 clique-cover problem, and for perfect graphs, the maximum q-colorable subgraph problems as special cases. This paper gives complexity results for the problem on subclasses of chordal graphs, e.g., strongly chordal graphs, k-trees, split graphs, and undirected path graphs.