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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.

05C75 Structural characterization of families of graphs