Claw-free graphs. III. Circular interval graphs

نویسندگان

Maria Chudnovsky

Paul D. Seymour

چکیده

Construct a graph as follows. Take a circle, and a collection of intervals from it, no three of which have union the entire circle; take a finite set of points V from the circle; and make a graph with vertex set V in which two vertices are adjacent if they both belong to one of the intervals. Such graphs are “circular interval graphs”, and they form an important subclass of the class of all claw-free graphs. In this paper we characterize them by excluded induced subgraphs. This is a step towards the main goal of this series, to find a structural characterization of all claw-free graphs.

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