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I've constructed a graph in a simular way an interval graph would be constructed from the overlap of intervals. But my intervals are from a modular domain.

Modular overlap

Given $\mathit{interval} \equiv \mathit{chordal} \cap \mathit{cocomparability}$ it is obvious the above graph is not an interval graph since it is not chordal. See cycle 2-4-5-6-1-7-2.

My question: is this just a cocomparability graph or does it fall under another classification?

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    No idea. As I said, I just found this through a quick Google search for "interval graph on a circle" or something like that. The Wikipedia article has a lot of references which might help.2012-02-09

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The circular arc graphs are a superset of the interval graphs, where rather than being intervals on a line, the vertices are represented as arcs around a circle. As you noticed, the chordless cycles are not forbidden subgraphs for the circular-arc graphs.