Abstract
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.
Highlights
Consider a finite family of non-empty sets
The intersection graph of this family is obtained by representing each set by a vertex, two vertices being connected by an edge if and only if the corresponding sets intersect
For t 1, a graph G is t-self-clique if Kt (G)
Summary
Consider a finite family of non-empty sets. The intersection graph of this family is obtained by representing each set by a vertex, two vertices being connected by an edge if and only if the corresponding sets intersect.A clique in a graph is a complete subgraph maximal under inclusion. For t 1, a graph G is t-self-clique if Kt (G) A circular-arc graph is the intersection graph of a family of arcs of a circle. A circular-arc model of a graph is proper if no arc is included in another.
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