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On graphsG for which all large trees areG-good

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Abstract

LetG be a graph satisfying x(G) = k. The following problem is considered: WhichG have the property that, if n is large enough, the Ramsey numberr(G, T) has the value (k — 1)(n — 1) + 1 for all treesT onn vertices? It is shown thatG has this property if and only if for somem, G is a subgraph of bothL k,m andM K.m , whereL k,m andM k,m are two particulark-chromatic graphs. Indeed, it is shown thatr(L k,m ,M k,m ,T n ) = (k — 1)(n — 1) + 1 whenn is large.

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Authors and Affiliations

  1. Department of Computer Science, City College, C.U.N.Y., 10031, New York, NY, USA

    Stefan A. Burr

  2. Department of Mathematic Science, Memphis State University, 8152, Memphis, TN, USA

    Ralph J. Faudree

Authors
  1. Stefan A. Burr
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  2. Ralph J. Faudree
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This research was supported in part by ONR Grant N00014-85-K-0704 and PSC-CUNY Grant 6-65227.

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Burr, S.A., Faudree, R.J. On graphsG for which all large trees areG-good. Graphs and Combinatorics 9, 305–313 (1993). https://doi.org/10.1007/BF02988318

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  • DOI: https://doi.org/10.1007/BF02988318

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