Decomposing Berge Graphs Containing No Proper Wheel, Long Prism Or Their Complements

In this paper we show that, if G is a Berge graph such that neither G nor its complement \( \ifmmode\expandafter\bar\else\expandafter\=\fi{G} \) contains certain induced subgraphs, named proper wheels and long prisms, then either G is a basic perfect graph( a bipartite graph, a line graph of a bipartite graph or the complement of such graphs) or it has a skew partition that cannot occur in a minimally imperfect graph. This structural result implies that G is perfect.

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Correspondence to Michele Conforti.

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This work was supported in part by NSF grant DMI-0352885 and ONR grant N00014-03-1-0188.

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Conforti, M., Cornuéjols, G. & Zambelli, G. Decomposing Berge Graphs Containing No Proper Wheel, Long Prism Or Their Complements. Combinatorica 26, 533–558 (2006). https://doi.org/10.1007/s00493-006-0031-0

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Mathematics Subject Classification (2000):

  • 05C17