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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics