Ramsey numbers for the pair sparse graph-path or cycle

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

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20 Citations (Scopus)


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
Issue number2
Publication statusPublished - 1982


ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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