The Ramsey number of a graph with bounded maximum degree

C. Chvatál, V. Rödl, E. Szemerédi, W. T. Trotter

Research output: Contribution to journalArticle

90 Citations (Scopus)

Abstract

The Ramsey number of a graph G is the least number t for which it is true that whenever the edges of the complete graph on t vertices are colored in an arbitrary fashion using two colors, say red and blue, then it is always the case that either the red subgraph contains G or the blue subgraph contains G. A conjecture of P. Erdös and S. Burr is settled in the affirmative by proving that for each d ≥ 1, there exists a constant c so that if G is any graph on n vertices with maximum degree d, then the Ramsey number of G is at most cn.

Original languageEnglish
Pages (from-to)239-243
Number of pages5
JournalJournal of Combinatorial Theory. Series B
Volume34
Issue number3
DOIs
Publication statusPublished - 1983

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Ramsey number
Maximum Degree
Subgraph
Color
Graph in graph theory
Complete Graph
Arbitrary

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

The Ramsey number of a graph with bounded maximum degree. / Chvatál, C.; Rödl, V.; Szemerédi, E.; Trotter, W. T.

In: Journal of Combinatorial Theory. Series B, Vol. 34, No. 3, 1983, p. 239-243.

Research output: Contribution to journalArticle

Chvatál, C. ; Rödl, V. ; Szemerédi, E. ; Trotter, W. T. / The Ramsey number of a graph with bounded maximum degree. In: Journal of Combinatorial Theory. Series B. 1983 ; Vol. 34, No. 3. pp. 239-243.
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