Linear upper bounds for local Ramsey numbers

Miroslaw Truszczynski, Z. Tuza

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

A coloring of the edges of a graph is called a local k-coloring if every vertex is incident to edges of at most k distinct colors. For a given graph G, the local Ramsey number, rlock(G), is the smallest integer n such that any local k-coloring of Kn, (the complete graph on n vertices), contains a monochromatic copy of G. The following conjecture of Gyárfás et al. is proved here: for each positive integer k there exists a constant c = c(k) such that rlock(G) ≤ crk(G), for every connected grraph G (where rk(G) is the usual Ramsey number for k colors). Possible generalizations for hypergraphs are considered.

Original languageEnglish
Pages (from-to)67-73
Number of pages7
JournalGraphs and Combinatorics
Volume3
Issue number1
DOIs
Publication statusPublished - Dec 1987

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Ramsey number
Coloring
Colouring
Upper bound
Color
Integer
Graph in graph theory
Hypergraph
Complete Graph
Distinct
Vertex of a graph

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Mathematics(all)

Cite this

Linear upper bounds for local Ramsey numbers. / Truszczynski, Miroslaw; Tuza, Z.

In: Graphs and Combinatorics, Vol. 3, No. 1, 12.1987, p. 67-73.

Research output: Contribution to journalArticle

Truszczynski, Miroslaw ; Tuza, Z. / Linear upper bounds for local Ramsey numbers. In: Graphs and Combinatorics. 1987 ; Vol. 3, No. 1. pp. 67-73.
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