Upper chromatic number of Steiner triple and quadruple systems

Lorenzo Milazzo, Z. Tuza

Research output: Contribution to journalArticle

49 Citations (Scopus)

Abstract

The upper chromatic number χ̄(ℋ) of a set system ℋ is the maximum number of colours that can be assigned to the elements of the underlying set of ℋ in such a way that each H ∈ ℋ contains a monochromatic pair of elements. We prove that a Steiner triple system of order ν≤2k - 1 has an upper chromatic number which is at most k. This bound is the best possible, and the extremal configurations attaining equality can be characterized. Some consequences for Steiner quadruple systems are also obtained.

Original languageEnglish
Pages (from-to)247-259
Number of pages13
JournalDiscrete Mathematics
Volume174
Issue number1-3
Publication statusPublished - Sep 15 1997

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Steiner Quadruple System
Steiner Triple System
Chromatic number
Color
Set Systems
Equality
Configuration

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Upper chromatic number of Steiner triple and quadruple systems. / Milazzo, Lorenzo; Tuza, Z.

In: Discrete Mathematics, Vol. 174, No. 1-3, 15.09.1997, p. 247-259.

Research output: Contribution to journalArticle

Milazzo, Lorenzo ; Tuza, Z. / Upper chromatic number of Steiner triple and quadruple systems. In: Discrete Mathematics. 1997 ; Vol. 174, No. 1-3. pp. 247-259.
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