Logarithmic upper bound for the upper chromatic number of S(t, t + 1,v) systems

Lorenzo Milazzo, Z. Tuza

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Vertex colorings of Steiner systems S(t,t + l,v) are considered in which each block contains at least two vertices of the same color. Necessary conditions for the existence of such colorings with given parameters are determined, and an upper bound of the order O(ln v) is found for the maximum number of colors. This bound remains valid for nearly complete partial Steiner systems, too. In striking contrast, systems S(t,k,v) with k ≥ t + 2 always admit colorings with at least c · v a colors, for some positive constants c and α, as v → ∞.

Original languageEnglish
Pages (from-to)213-223
Number of pages11
JournalArs Combinatoria
Volume92
Publication statusPublished - Jul 2009

Fingerprint

Chromatic number
Steiner System
Logarithmic
Upper bound
Colouring
S-system
Vertex Coloring
Valid
Partial
Necessary Conditions
Color

Keywords

  • Mixed hypergraph
  • Steiner system
  • Upper chromatic number
  • Vertex coloring

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Logarithmic upper bound for the upper chromatic number of S(t, t + 1,v) systems. / Milazzo, Lorenzo; Tuza, Z.

In: Ars Combinatoria, Vol. 92, 07.2009, p. 213-223.

Research output: Contribution to journalArticle

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