A note on covering edge colored hypergraphs by monochromatic components

Shinya Fujita, Michitaka Furuya, A. Gyárfás, Ágnes Tóth

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

For r≥2, α≥r-1 and k≥1, let c(r,α,k be the smallest integer c such that the vertex set of any non-trivial r-uniform k-edge-colored hypergraph H with α(H=α can be covered by c monochromatic connected components. Here α(H is the maximum cardinality of a subset A of vertices in H such that A does not contain any edges. An old conjecture of Ryser is equivalent to c(2,α,k=α(r-1 and a recent result of Z. Király states that c(r,r-1,k=⌈/kr⌉ for any r≥3. Here we make the first step to treat non-complete hypergraphs, showing that c(r,r,r=2 for r≥2 and c(r,r,r+1=3 for r≥3.

Original languageEnglish
Article numberP2.33
JournalElectronic Journal of Combinatorics
Volume21
Issue number2
Publication statusPublished - May 13 2014

Fingerprint

Hypergraph
Covering
Connected Components
Cardinality
Integer
Subset
Vertex of a graph

Keywords

  • Edge-coloring
  • Graph theory
  • Monochromatic component

ASJC Scopus subject areas

  • Geometry and Topology
  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

A note on covering edge colored hypergraphs by monochromatic components. / Fujita, Shinya; Furuya, Michitaka; Gyárfás, A.; Tóth, Ágnes.

In: Electronic Journal of Combinatorics, Vol. 21, No. 2, P2.33, 13.05.2014.

Research output: Contribution to journalArticle

Fujita, Shinya ; Furuya, Michitaka ; Gyárfás, A. ; Tóth, Ágnes. / A note on covering edge colored hypergraphs by monochromatic components. In: Electronic Journal of Combinatorics. 2014 ; Vol. 21, No. 2.
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