Normal hypergraphs and the perfect graph conjecture

Research output: Contribution to journalArticle

435 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)253-267
Number of pages15
JournalDiscrete Mathematics
Volume2
Issue number3
DOIs
Publication statusPublished - 1972

Fingerprint

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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Normal hypergraphs and the perfect graph conjecture. / Lovász, L.

In: Discrete Mathematics, Vol. 2, No. 3, 1972, p. 253-267.

Research output: Contribution to journalArticle

@article{0a2e96fd8d5f4492ba15d40018aa2766,
title = "Normal hypergraphs and the perfect graph conjecture",
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.",
author = "L. Lov{\'a}sz",
year = "1972",
doi = "10.1016/0012-365X(72)90006-4",
language = "English",
volume = "2",
pages = "253--267",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "3",

}

TY - JOUR

T1 - Normal hypergraphs and the perfect graph conjecture

AU - Lovász, L.

PY - 1972

Y1 - 1972

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=49649140846&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49649140846&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(72)90006-4

DO - 10.1016/0012-365X(72)90006-4

M3 - Article

AN - SCOPUS:49649140846

VL - 2

SP - 253

EP - 267

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 3

ER -