SIAM Journal on Discrete Mathematics
Degree Ramsey numbers for cycles and blowups of trees
European Journal of Combinatorics
Letting Alice and Bob choose which problem to solve: Implications to the study of cellular automata
Theoretical Computer Science
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We consider the following question: how large does n haveto be to guarantee that in any two-coloring of the edges of thecomplete graph Kn,n there is amonochromatic Kk,k? In the late 1970s,Irving showed that it was sufficient, for k large, thatn ≥ 2k - 1 (k - 1) - 1. Here weimprove upon this bound, showing that it is sufficient to take$${n} \geq ({1} + {o}({1})) {2}^{{k}+ {1}}\; {\log}\; {k},$$ wherethe log is taken to the base 2. © 2008 Wiley Periodicals, Inc.J Graph Theory 58: 351356, 2008