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Characterisations of Intersection Graphs by Vertex Orderings

David R. Wood
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Abstract

Characterisations of interval graphs, comparability graphs, co-comparability graphs, permutation graphs, and split graphs in terms of linear orderings of the vertex set are presented. As an application, it is proved that interval graphs, co-comparability graphs, AT-free graphs, and split graphs have bandwidth bounded by their maximum degree.

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David R. Wood. 2004-04-14. Characterisations of Intersection Graphs by Vertex Orderings. https://arxiv.org/abs/cs/0404031

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