Edge coloring complete uniform hypergraphs with many components

Yair Caro; Raphael Yuster

doi:10.1016/j.jctb.2004.01.002

Edge coloring complete uniform hypergraphs with many components

Yair Caro, Raphael Yuster

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let H be a hypergraph. For a k-edge coloring c:E(H)→{1,..,k} let f(H,c) be the number of components in the subhypergraph induced by the color class with the least number of components. Let f_k(H) be the maximum possible value of f(H,c) ranging over all k-edge colorings of H. If H is the complete graph K_n then, trivially, f₁(K_n)=f₂ (K_n)=1. In this paper we prove that for n≥6,f₃ (K_n)=⌊n/6⌋+1 and supply close upper and lower bounds for f_k(K_n) in case k≥4. Several results concerning the value of f_k(K_n^r), where K_n^r is the complete r-uniform hypergraph on n vertices, are also established.

Original language	English
Pages (from-to)	215-227
Number of pages	13
Journal	Journal of Combinatorial Theory. Series B
Volume	91
Issue number	2
DOIs	https://doi.org/10.1016/j.jctb.2004.01.002
State	Published - Jul 2004

Keywords

Coloring
Components
Hypergraph

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jctb.2004.01.002

Cite this

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abstract = "Let H be a hypergraph. For a k-edge coloring c:E(H)→{1,..,k} let f(H,c) be the number of components in the subhypergraph induced by the color class with the least number of components. Let fk(H) be the maximum possible value of f(H,c) ranging over all k-edge colorings of H. If H is the complete graph Kn then, trivially, f1(Kn)=f2 (Kn)=1. In this paper we prove that for n≥6,f3 (Kn)=⌊n/6⌋+1 and supply close upper and lower bounds for fk(Kn) in case k≥4. Several results concerning the value of fk(Knr), where Knr is the complete r-uniform hypergraph on n vertices, are also established.",

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author = "Yair Caro and Raphael Yuster",

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AU - Caro, Yair

AU - Yuster, Raphael

PY - 2004/7

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AB - Let H be a hypergraph. For a k-edge coloring c:E(H)→{1,..,k} let f(H,c) be the number of components in the subhypergraph induced by the color class with the least number of components. Let fk(H) be the maximum possible value of f(H,c) ranging over all k-edge colorings of H. If H is the complete graph Kn then, trivially, f1(Kn)=f2 (Kn)=1. In this paper we prove that for n≥6,f3 (Kn)=⌊n/6⌋+1 and supply close upper and lower bounds for fk(Kn) in case k≥4. Several results concerning the value of fk(Knr), where Knr is the complete r-uniform hypergraph on n vertices, are also established.

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Edge coloring complete uniform hypergraphs with many components

Abstract

Keywords

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