1982•Journal of Graph TheoryRequires access

A relationship between triangulated graphs, comparability graphs, proper interval graphs, proper circular‐arc graphs, and nested interval graphs

Dale J. Skrien

Abstract

Abstract Given a set F of digraphs, we say a graph G is a F‐graph (resp., F*‐graph) if it has an orientation (resp., acyclic orientation) that has no induced subdigraphs isomorphic to any of the digraphs in F. It is proved that all the classes of graphs mentioned in the title are F‐graphs or F*‐graphs for subsets F of a set of three digraphs.

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Key concepts: Combinatorics, Mathematics, Indifference graph, Interval graph, Pathwidth, Chordal graph, Split graph, Block graph