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Self-clique Helly circular-arc graphs. (English) Zbl 1087.05042
Summary: A clique in a graph is a complete subgraph maximal under inclusion. The clique graph of a graph is the intersection graph of its cliques. A graph is self-clique when it is isomorphic to its clique graph. A circular-arc graph is the intersection graph of a family of arcs of a circle. A Helly circular-arc graph is a circular-arc graph admitting a model whose arcs satisfy the Helly property. In this note, we describe all the self-clique Helly circular-arc graphs.

MSC:
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
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