### 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 language | English |
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Pages (from-to) | 29-42 |

Number of pages | 14 |

Journal | North-Holland Mathematics Studies |

Volume | 88 |

Issue number | C |

DOIs | |

Publication status | Published - 1984 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

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

Research output: Contribution to journal › Article

*North-Holland Mathematics Studies*, vol. 88, no. C, pp. 29-42. https://doi.org/10.1016/S0304-0208(08)72920-7

}

TY - JOUR

T1 - Normal Hypergraphs and the Weak Perfect Graph Conjecture

AU - Lovász, L.

PY - 1984

Y1 - 1984

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77956900669&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77956900669&partnerID=8YFLogxK

U2 - 10.1016/S0304-0208(08)72920-7

DO - 10.1016/S0304-0208(08)72920-7

M3 - Article

AN - SCOPUS:77956900669

VL - 88

SP - 29

EP - 42

JO - North-Holland Mathematics Studies

JF - North-Holland Mathematics Studies

SN - 0304-0208

IS - C

ER -