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Large generalized books are p-good

Vladimir Nikiforov·Cecil Rousseau
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Abstract

An r-book of size q is a union of q (r+1)-cliques sharing a common r-clique. We find exactly the Ramsey number of a p-clique versus r-books of sufficiently large size. Furthermore, we find asymptotically the Ramsey number of any fixed p-chromatic graph versus r-books of sufficiently large size. The key element in our proofs is Szemeredi's Regularity Lemma.

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Vladimir Nikiforov, Cecil Rousseau. 2004-05-07. Large generalized books are p-good. https://arxiv.org/abs/math/0405140

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