Normal hypergraphs and the perfect graph conjecture

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4 Citations (Scopus)

Abstract

A hypergraph is called normal if the chromatic index of any partial hypergraph H of it coincides with the maximum valency in H. It is proved that a hypergraph is normal iff the maximum number of disjoint hyperedges coincides with the minimum number of vertices representing the hyperedges in each partial hypergraph of it. This theorem implies the following conjecture of Berge: The complement of a perfect graph is perfect. A new proof is given for a related theorem of Berge and Las Vergnas. Finally, the results are applied on a problem of integer valued linear programming, slightly sharpening some results of Fulkerson.

Original languageEnglish
Pages (from-to)867-875
Number of pages9
JournalDiscrete Mathematics
Volume306
Issue number10-11
DOIs
Publication statusPublished - May 28 2006

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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