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 ⩽ r i ⩽ ¦C i¦ . The generalized clique transversal problem is to determine the minimum cardinality of a subset D of V such that ¦D ∩ C i¦ ⩾ 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.