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Multicolor bipartite Ramsey number of C4 and large Kn, n

✍ Scribed by Qizhong Lin; Yusheng Li

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 92 KB
Volume: 67
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20512

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✦ Synopsis

Let br k (C 4 ; K n,n ) be the smallest N such that if all edges of K N,N are colored by k +1 colors, then there is a monochromatic C 4 in one of the first k colors or a monochromatic K n,n in the last color. It is shown that br k (C 4 ; K n,n ) = (n 2 / log 2 n) for k ≥ 3, and br 2 (C 4 ; K n,n ) ≥ c(n log log n / log 2 n) 2 for large n. The main part of the proof is an algorithm to bound the number of large K n,n in quasi-random graphs.

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