Recognizing Berge Graphs

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.

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Correspondence to Maria Chudnovsky*.

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* Currently this author is a Clay Mathematics Institute Research Fellow.

** Supported by NSF grant DMI-0352885 and ONR grant N00014-97-1-0196.

† Supported by ONR grant N00014-01-1-0608, and NSF grant DMS-0070912.

‡ Supported by EPSRC grant GR/R35629/01.

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Chudnovsky*, M., Cornuéjols**, G., Liu†, X. et al. Recognizing Berge Graphs. Combinatorica 25, 143–186 (2005). https://doi.org/10.1007/s00493-005-0012-8

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Mathematics Subject Classification (2000):

  • 05C17