Ramsey numbers for the pair sparse graph-path or cycle

S. A. Burr, P. Erdős, R. J. Faudree, C. C. Rousseau, R. H. Schelp

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

Let G be a connected graph on n vertices with no more than n(\ + e) edges, and Pkor Cka path or cycle with k vertices. In this paper we will show that if n is sufficiently large and e is sufficiently small then for k odd r(G> Ck) = In - 1. Also, for k > 2, r(G, pk) _ max(n + [k/2] — 1, n + k - 2 — α' - δ), where a' is the independence number of an appropriate subgraph of G and 6 is 0 or 1 depending upon /t, k and a.

Original languageEnglish
Pages (from-to)501-512
Number of pages12
JournalTransactions of the American Mathematical Society
Volume269
Issue number2
DOIs
Publication statusPublished - 1982

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Ramsey number
Independence number
Sparse Graphs
Connected graph
Subgraph
Odd
Cycle
Path

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Ramsey numbers for the pair sparse graph-path or cycle. / Burr, S. A.; Erdős, P.; Faudree, R. J.; Rousseau, C. C.; Schelp, R. H.

In: Transactions of the American Mathematical Society, Vol. 269, No. 2, 1982, p. 501-512.

Research output: Contribution to journalArticle

Burr, S. A. ; Erdős, P. ; Faudree, R. J. ; Rousseau, C. C. ; Schelp, R. H. / Ramsey numbers for the pair sparse graph-path or cycle. In: Transactions of the American Mathematical Society. 1982 ; Vol. 269, No. 2. pp. 501-512.
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