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Clique graphs of Helly circular-arc graphs. (English) Zbl 1072.05565
A graph $$G$$ is a Helly circular-arc graph if $$G$$ can be represented as the intersection graph of a system of arcs on a circle such that the arcs satisfy the Helly property. The clique graph of $$G$$ is the intersection graph of the cliques of $$G$$. In the paper, clique graphs of Helly circular-arc graphs are characterized in terms of the existence of a certain circular ordering of the vertex set. As a corollary it is shown that the class of clique graphs of Helly circular-arc graphs is properly contained in the intersection of Helly circular-arc graphs, clique-Helly circular-arc graphs and proper circular-arc graphs.

##### MSC:
 05C75 Structural characterization of families of graphs
##### Keywords:
Helly circular-arc graph; intersection graph