Normal Hypergraphs and the Weak Perfect Graph Conjecture

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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)29-42
Number of pages14
JournalNorth-Holland Mathematics Studies
Volume88
Issue numberC
DOIs
Publication statusPublished - 1984

Fingerprint

Perfect Graphs
Hypergraph
Partial
Chromatic Index
Theorem
Linear programming
Disjoint
Complement
Imply
Integer

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Normal Hypergraphs and the Weak Perfect Graph Conjecture. / Lovász, L.

In: North-Holland Mathematics Studies, Vol. 88, No. C, 1984, p. 29-42.

Research output: Contribution to journalArticle

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