A note on Ramsey Numbers for Books
A book of size N is the union of N triangles sharing a common edge. We show that the Ramsey number of a book of size N vs. a book of size M equals 2N+3 for all N>(10^6)M. Our proof is based on counting.
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arXiv subjects
Cecil Rousseau
Publications and source records attributed to Cecil Rousseau.
Large generalized books are p-good
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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Book Ramsey numbers I
A book of size q is the union of q triangles sharing a common edge. We find the exact Ramsey number of books of size q versus books of size p when p<q/6-o(q).
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