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arXiv · 1110.4205

A Tur'an-type problem for circular arc graphs

Rosalie Carlson·Stephen Flood·Kevin O'Neill·Francis Edward Su
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Abstract

A circular arc graph is the intersection graph of a collection of connected arcs on the circle. We solve a Tur'an-type problem for circular arc graphs: for n arcs, if m and M are the minimum and maximum number of arcs that contain a common point, what is the maximum number of edges the circular arc graph can contain? We establish a sharp bound and produce a maximal construction. For a fixed m, this can be used to show that if the circular arc graph has enough edges, there must be a point that is covered by at least M arcs. In the case m=0, we recover results for interval graphs established by Abbott and Katchalski (1979). We suggest applications to voting situations with interval or circular political spectra.

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Rosalie Carlson, Stephen Flood, Kevin O'Neill, Francis Edward Su. 2011-10-19. A Tur'an-type problem for circular arc graphs. https://arxiv.org/abs/1110.4205

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