Hypergraph coverings and local colorings

Yair Caro, Z. Tuza

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

If the edge sets of some r-uniform hypergraphs H1, ..., Ht contain all the r-tuples of an n-element set, and each Hi has chromatic number at most k, then for the sum of the orders of the Hi we have Σ|V(Hi)| ≥ (n log ( n (r - 1))) log k. In particular, if Knr has an edge coloring such that each vertex is incident to edges of at most s colors and every monochromatic class of edges forms a k-vertex-colorable hypergraph, then n ≤ (r - 1) ks. Both bounds are sharp.

Original languageEnglish
Pages (from-to)79-85
Number of pages7
JournalJournal of Combinatorial Theory. Series B
Volume52
Issue number1
DOIs
Publication statusPublished - 1991

Fingerprint

Coloring
Hypergraph
Colouring
Covering
Color
Uniform Hypergraph
Edge Coloring
Vertex of a graph
Chromatic number
Class
Form

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Hypergraph coverings and local colorings. / Caro, Yair; Tuza, Z.

In: Journal of Combinatorial Theory. Series B, Vol. 52, No. 1, 1991, p. 79-85.

Research output: Contribution to journalArticle

@article{0ab85a80ff144d5680f7be04d2e6924f,
title = "Hypergraph coverings and local colorings",
abstract = "If the edge sets of some r-uniform hypergraphs H1, ..., Ht contain all the r-tuples of an n-element set, and each Hi has chromatic number at most k, then for the sum of the orders of the Hi we have Σ|V(Hi)| ≥ (n log ( n (r - 1))) log k. In particular, if Knr has an edge coloring such that each vertex is incident to edges of at most s colors and every monochromatic class of edges forms a k-vertex-colorable hypergraph, then n ≤ (r - 1) ks. Both bounds are sharp.",
author = "Yair Caro and Z. Tuza",
year = "1991",
doi = "10.1016/0095-8956(91)90092-X",
language = "English",
volume = "52",
pages = "79--85",
journal = "Journal of Combinatorial Theory. Series B",
issn = "0095-8956",
publisher = "Academic Press Inc.",
number = "1",

}

TY - JOUR

T1 - Hypergraph coverings and local colorings

AU - Caro, Yair

AU - Tuza, Z.

PY - 1991

Y1 - 1991

N2 - If the edge sets of some r-uniform hypergraphs H1, ..., Ht contain all the r-tuples of an n-element set, and each Hi has chromatic number at most k, then for the sum of the orders of the Hi we have Σ|V(Hi)| ≥ (n log ( n (r - 1))) log k. In particular, if Knr has an edge coloring such that each vertex is incident to edges of at most s colors and every monochromatic class of edges forms a k-vertex-colorable hypergraph, then n ≤ (r - 1) ks. Both bounds are sharp.

AB - If the edge sets of some r-uniform hypergraphs H1, ..., Ht contain all the r-tuples of an n-element set, and each Hi has chromatic number at most k, then for the sum of the orders of the Hi we have Σ|V(Hi)| ≥ (n log ( n (r - 1))) log k. In particular, if Knr has an edge coloring such that each vertex is incident to edges of at most s colors and every monochromatic class of edges forms a k-vertex-colorable hypergraph, then n ≤ (r - 1) ks. Both bounds are sharp.

UR - http://www.scopus.com/inward/record.url?scp=44949281902&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=44949281902&partnerID=8YFLogxK

U2 - 10.1016/0095-8956(91)90092-X

DO - 10.1016/0095-8956(91)90092-X

M3 - Article

AN - SCOPUS:44949281902

VL - 52

SP - 79

EP - 85

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

IS - 1

ER -