A Ramsey problem of Harary on graphs with prescribed size

P. Erdös, R. J. Faudree, C. C. Rousseau, R. H. Schelp

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Abstract

Lower bounds on the Ramsey number r(G, H), as a function of the size ofthe graphs G and H, are determined. In particular, if H is a graph with n lines, lower bounds for r(H) = r(H,H) and r(Km, H) are calculated in terms of n in the first case and m and n in the second case. For m = 3 an upper bound is also determined. These results partially answer a question raised by Harary about the relationship between Ramsey numbers and the size of graphs.

Original languageEnglish
Pages (from-to)227-233
Number of pages7
JournalDiscrete Mathematics
Volume67
Issue number3
DOIs
Publication statusPublished - Dec 1987

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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