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Ramsey Size Linear Graphs

  • Paul Erdős (a1), R. J. Faudree (a2), C. C. Rousseau (a2) and R. H. Schelp (a2)
Abstract

A graph G is Ramsey size linear if there is a constant C such that for any graph H with n edges and no isolated vertices, the Ramsey number r(G, H)Cn. It will be shown that any graph G with p vertices and q ≥ 2p − 2 edges is not Ramsey size linear, and this bound is sharp. Also, if G is connected and qp + 1, then G is Ramsey size linear, and this bound is sharp also. Special classes of graphs will be shown to be Ramsey size linear, and bounds on the Ramsey numbers will be determined.

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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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