Normal hypergraphs and the perfect graph conjecture

doi:10.1016/j.disc.2006.03.007

Discrete Mathematics

Volume 306, Issues 10–11, 28 May 2006, Pages 867-875

https://doi.org/10.1016/j.disc.2006.03.007 Get rights and content

Under an Elsevier user license

open archive

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.

Cited by (0)

: DOI of original article: 10.1016/0012-365X(72)90006-4

: The original article was published in Discrete Mathematics 2 (1972) 253–267