Recognizing Berge Graphs

Authors:
Maria Chudnovsky;Gérard Cornuéjols;Xinming Liu;Paul Seymour;Kristina Vušković
Affiliations:
Mathematics Dept, Princeton University, Fine Hall, Princeton, NJ 08544, USA;-;Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA 15213, USA;Mathematics Dept, Princeton University, Fine Hall, Princeton, NJ 08544, USA;School of Computing, University of Leeds, Leeds LS2 9JT, UK
Venue:
Combinatorica
Year:
2005

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Abstract

A graph is Berge if no induced subgraph of G is an odd cycle of length at least five or the complement of one. In this paper we give an algorithm to test if a graph G is Berge, with running time O(|V (G)|9). This is independent of the recent proof of the strong perfect graph conjecture.