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1988•Journal of Graph TheoryRequires access

Threshold tolerance graphs

Clyde Monma, Bruce Reed, William T. Trotter

Open publisher page 33 citations

Abstract

Abstract In this paper, we introduce a class of graphs that generalize threshold graphs by introducing threshold tolerances. Several characterizations of these graphs are presented, one of which leads to a polynomial‐time recognition algorithm. It is also shown that the complements of these graphs contain interval graphs and threshold graphs, and are contained in the subclass of chordal graphs called strongly chordal graphs, and in the class of interval tolerance graphs.

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What this paper is about

Abstract In this paper, we introduce a class of graphs that generalize threshold graphs by introducing threshold tolerances. Several characterizations of these graphs are presented, one of which leads to a polynomial‐time recognition algorithm. It is also shown that the complements of these graphs contain interval graphs and threshold graphs, and are contained in the subclass of chordal graphs called strongly chordal graphs, and in the class of interval tolerance graphs.

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Available abstract

Abstract In this paper, we introduce a class of graphs that generalize threshold graphs by introducing threshold tolerances. Several characterizations of these graphs are presented, one of which leads to a polynomial‐time recognition algorithm. It is also shown that the complements of these graphs contain interval graphs and threshold graphs, and are contained in the subclass of chordal graphs called strongly chordal graphs, and in the class of interval tolerance graphs.

Key concepts: Chordal graph, Indifference graph, Interval graph, Combinatorics, Mathematics, Pathwidth, Maximal independent set, Clique-sum

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