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arXiv · 1502.06175

New representation results for planar graphs

Farhad Shahrokhi
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Abstract

A universal representation theorem is derived that shows any graph is the intersection graph of one chordal graph, a number of co-bipartite graphs, and one unit interval graph. Central to the the result is the notion of the clique cover width which is a generalization of the bandwidth parameter. Specifically, we show that any planar graph is the intersection graph of one chordal graph, four co-bipartite graphs, and one unit interval graph. Equivalently, any planar graph is the intersection graph of a chordal graph and a graph that has {clique cover width} of at most seven. We further describe the extensions of the results to graphs drawn on surfaces and graphs excluding a minor of crossing number of at most one.

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Farhad Shahrokhi. 2015-02-22. New representation results for planar graphs. https://arxiv.org/abs/1502.06175

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