Edge coloring complete uniform hypergraphs with many components

Yair Caro, Raphael Yuster

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)215-227
Number of pages13
JournalJournal of Combinatorial Theory. Series B
Issue number2
StatePublished - Jul 2004


  • Coloring
  • Components
  • Hypergraph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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