Ramsey theory on Steiner triples

Elliot Granath, A. Gyárfás, Jerry Hardee, Trent Watson, Xiaoze Wu

Research output: Contribution to journalArticle

Abstract

We call a partial Steiner triple system C (configuration) t-Ramsey if for large enough n (in terms of (Formula presented.)), in every t-coloring of the blocks of any Steiner triple system STS(n) there is a monochromatic copy of C. We prove that configuration C is t-Ramsey for every t in three cases: C is acyclic every block of C has a point of degree one C has a triangle with blocks 123, 345, 561 with some further blocks attached at points 1 and 4 This implies that we can decide for all but one configurations with at most four blocks whether they are t-Ramsey. The one in doubt is the sail with blocks 123, 345, 561, 147.

Original languageEnglish
Pages (from-to)5-11
Number of pages7
JournalJournal of Combinatorial Designs
Volume26
Issue number1
DOIs
Publication statusPublished - Jan 1 2018

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Ramsey Theory
Steiner Triple System
Configuration
Colouring
Triangle
Partial
Imply

Keywords

  • Ramsey theory
  • Steiner triples

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

Ramsey theory on Steiner triples. / Granath, Elliot; Gyárfás, A.; Hardee, Jerry; Watson, Trent; Wu, Xiaoze.

In: Journal of Combinatorial Designs, Vol. 26, No. 1, 01.01.2018, p. 5-11.

Research output: Contribution to journalArticle

Granath, E, Gyárfás, A, Hardee, J, Watson, T & Wu, X 2018, 'Ramsey theory on Steiner triples', Journal of Combinatorial Designs, vol. 26, no. 1, pp. 5-11. https://doi.org/10.1002/jcd.21585
Granath, Elliot ; Gyárfás, A. ; Hardee, Jerry ; Watson, Trent ; Wu, Xiaoze. / Ramsey theory on Steiner triples. In: Journal of Combinatorial Designs. 2018 ; Vol. 26, No. 1. pp. 5-11.
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