Covering and coloring polygon-circle graphs

Abstract

Polygon-circle graphs are intersection graphs of polygons inscribed in a circle. This class of graphs includes circle graphs (intersection graphs of chords of a circle), circular arc graphs (intersection graphs of arcs on a circle), chordal graphs and outerplanar graphs. We investigate binding functions for chromatic number and clique covering number of polygon-circle graphs in terms of their clique and independence numbers. The bound ~ log ~, for the clique covering number is asymptotically best possible. For chromatic number, the upper bound we prove is of order 2 ~, which is better than previously known upper bounds for circle graphs.

DOI: 10.1016/S0012-365X(96)00344-5

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@article{Kostochka1997CoveringAC, title={Covering and coloring polygon-circle graphs}, author={Alexandr V. Kostochka and Jan Kratochv{\'i}l}, journal={Discrete Mathematics}, year={1997}, volume={163}, pages={299-305} }