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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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    The complement of the graph has a transitive ordering (1,4) (1,3) (1,2) (3,2) (6,2) (6,7) (5,2) (5,7)2012-02-09
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    A quick Google search led me to *[circular-arc graph](http://en.wikipedia.org/wiki/Circular-arc_graph)*. Is that what you want?2012-02-09
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    Thanks @RahulNarain, do you know any equivilance relations between circular-arc graphs and other classes of graphs?2012-02-09
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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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