A graph G is a circular-arc graph if it is the intersection graph of a set of arcs on a circle. That is, there is one arc for each vertex of G, and two vertices are adjacent in G if and only if the corresponding arcs intersect. We give a linear-time algorithm for recognizing this class of graphs. When G is a member of the class, the algorithm gives a certificate in the form of a set of arcs that realize it.
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McConnell, R. Linear-Time Recognition of Circular-Arc Graphs. Algorithmica 37, 93–147 (2003). https://doi.org/10.1007/s00453-003-1032-7
- Circular graph
- Interval graph
- Transitive orientation