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Upper Bounds for a Ramsey Theorem for Trees

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Abstract

For natural numbers n, k, r and s there exists a complete tree ? of height and arity\(r^{\left( {\mathop {K + 1}\limits_s } \right)} (n - 1) + 1\) such that for an arbitrary r-colouring of the s-chains of T a level-preserving monochromatically embedded copy of a complete tree of height k and arity n can be found in T. Moreover, a best possible upper bound for K is given.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Pretoria, 0002, Pretoria, South Africa

    C. J. Swanepoel & L. M. Pretorius

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  1. C. J. Swanepoel
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  2. L. M. Pretorius
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Swanepoel, C.J., Pretorius, L.M. Upper Bounds for a Ramsey Theorem for Trees. Graphs and Combinatorics 10, 377–382 (1994). https://doi.org/10.1007/BF02986688

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  • DOI: https://doi.org/10.1007/BF02986688

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