Reducing prime graphs and recognizing circle graphs

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1987 English Publisher:Springer Science and Business Media LLCJournal:Combinatorica, volume 7, pages 243-254 (issn: 0209-9683, eissn: 1439-6912,

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Authors: André Bouchet;

doi: 10.1007/bf02579301

Reducing prime graphs and recognizing circle graphs

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Abstract

A reduction theorem for prime (simple) graphs in \textit{W. H. Cunningham}'s sense [SIAM J. Algebraic Discrete Methods 3, 214-228 (1982; Zbl 0497.05031)] is presented. It says that every prime graph of order \(n>5\) contains a smaller prime graph of order n-1. As an application a polynomial algorithm for recognizing circle graphs in \((n^ 5)\) time is presented.

Related Organizations

University of Maine
France

Keywords

Directed graphs (digraphs), tournaments, reduction theorem, prime graph

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