Extendability conditions for Ramsey numbers and p-goodness of graphs release_dreljcwrqjcxrb7s7xw5bgotkm

by Jeremy F. Alm, Patrick Bahls

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2016  

Abstract

In their 2011 paper, Omidi and Raeisi give a condition that allows considerable extension of Ramsey numbers. We provide a new condition that is equivalent to the former one and show that the collection of graphs satisfying the latter condition is the set of all trees, enabling a new and elementary computation of the multicolor Ramsey number R(T,K_m_1,...,K_m_t) for trees T. We give a different proof of the result of Bohman and Keevash that the only connected graphs that are p-good for all p are trees. Finally, we develop a bound N = N(ℓ) such that for any connected graph H of girth ℓ, H is not p-good whenever p>N.
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Date   2016-10-28
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arXiv  1412.3071v2
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