Stability in circular arc graphs
Journal of Algorithms
An O(n log n+m log log n) maximum weight clique algorithm for circular-arc graphs
Information Processing Letters
Fibres and ordered set coloring
Journal of Combinatorial Theory Series A
Linear time algorithms on circular-arc graphs
Information Processing Letters
Algorithmic aspects of neighborhood numbers
SIAM Journal on Discrete Mathematics
Clique transversal and clique independence on comparability graphs
Information Processing Letters
Maximum h-colourable subgraph problem in balanced graphs
Information Processing Letters
SIAM Journal on Discrete Mathematics
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
The clique operator on circular-arc graphs
Discrete Applied Mathematics
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A circular-arc graph is the intersection graph of arcs on 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 polynomial time algorithms for finding the maximum cardinality and weight of a clique-independent set of a 3K2-free CA graph. Also, we apply the algorithms to the special case of an HCA graph. The complexity of the proposed algorithm for the cardinality problem in HCA graphs is O(n). This represents an improvement over the existing algorithm by Guruswami and Pandu Rangan, whose complexity is O(n2). These algorithms suppose that an HCA model of the graph is given.