Clique-independent sets of Helly circular-arc graphs

A circular-arc graph is the intersection graph of arcs of a circle. A Helly circular-arc graph is a circular-arc graph admitting a model whose arcs satisfy the Helly property. A clique-independent set of a graph is a set of pairwise disjoint cliques of the graph. It is NP-hard to compute the maximum cardinality of a clique-independent set for a general graph. In the present paper, we propose algorithms for finding the maximum cardinality and weight of a clique-independent set of a 3 K 2 ¯ -free CA graph. Also, we apply the algorithms to the special case of an H C A graph. The complexity of the proposed algorithm for the cardinality problem in H C A graphs is O(n). This represents an improvement over the existing algorithm, whose complexity is O ( n 2 ) .