Year: 2015
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Shahrokhi, Farhad
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1597094575