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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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1412.3071v2
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