Mono-multi bipartite Ramsey numbers, designs, and matrices

Paul N. Balister, A. Gyárfás, Jeno Lehel, Richard H. Schelp

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Eroh and Oellermann defined BRR (G1, G2) as the smallest N such that any edge coloring of the complete bipartite graph KN,N contains either a monochromatic G1 or a multicolored G2. We restate the problem of determining BRR (K1,λ, Kr,s) in matrix form and prove estimates and exact values for several choices of the parameters. Our general bound uses Füredi's result on fractional matchings of uniform hypergraphs and we show that it is sharp if certain block designs exist. We obtain two sharp results for the case r = s = 2: we prove BRR(K1,λ, K2,2) = 3λ - 2 and that the smallest n for which any edge coloring of Kλ,n contains either a monochromatic K1,λ or a multicolored K2,2 is λ2.

Original languageEnglish
Pages (from-to)101-112
Number of pages12
JournalJournal of Combinatorial Theory, Series A
Volume113
Issue number1
DOIs
Publication statusPublished - Jan 2006

Fingerprint

Ramsey number
Edge Coloring
Coloring
Uniform Hypergraph
Block Design
Complete Bipartite Graph
Fractional
Estimate
Design
Form

Keywords

  • 3-design
  • Extremal configurations
  • Mono- and multicolored bipartite graphs
  • Rainbow matrix
  • Ramsey theory

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Mono-multi bipartite Ramsey numbers, designs, and matrices. / Balister, Paul N.; Gyárfás, A.; Lehel, Jeno; Schelp, Richard H.

In: Journal of Combinatorial Theory, Series A, Vol. 113, No. 1, 01.2006, p. 101-112.

Research output: Contribution to journalArticle

Balister, Paul N. ; Gyárfás, A. ; Lehel, Jeno ; Schelp, Richard H. / Mono-multi bipartite Ramsey numbers, designs, and matrices. In: Journal of Combinatorial Theory, Series A. 2006 ; Vol. 113, No. 1. pp. 101-112.
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