Ramsey Numbers for Trees of Small Maximum Degree

Combinatorica volume 22, pages287–320(2002)Cite this article

For a tree T we write and , , for the sizes of the vertex classes of T as a bipartite graph. It is shown that for T with maximum degree , the obvious lower bound for the Ramsey number R(T,T) of is asymptotically the correct value for R(T,T).

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Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo; Waterloo, Ont., Canada N2L 3G1; E-mail: pehaxell@math.uwaterloo.ca, CA

    P. E. Haxell

  2. Department of Discrete Mathematics, Adam Mickiewicz University; ul. Matejki 48/49 60-769 Poznań, Poland; E-mail: tomasz@amu.edu.pl, PL

    T. Łuczak

  3. Department of Combinatorics and Optimization, University of Waterloo; Waterloo, Ont., Canada N2L 3G1; E-mail: pwtingle@undergrad.math.uwaterloo.ca, CA

    P. W. Tingley

Authors
  1. P. E. Haxell
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  2. T. Łuczak
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  3. P. W. Tingley
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Received December 15, 1999

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ID=" " The first and third authors were partially supported by NSERC. The second author was partially supported by KBN grant 2 P03A 021 17.

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Haxell, P., Łuczak, T. & Tingley, P. Ramsey Numbers for Trees of Small Maximum Degree. Combinatorica 22, 287–320 (2002). https://doi.org/10.1007/s004930200014

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  • AMS Subject Classification (2000) Classes:  05C05, 05C55