The bipartite k2,2-free process and bipartite ramsey number b(2, t)

Document Type

Article

Publication Date

1-1-2020

Journal / Book Title

Electronic Journal of Combinatorics

Abstract

The bipartite Ramsey number b(s, t) is the smallest integer n such that every blue-red edge coloring of Kn,n contains either a blue Ks,s or a red Kt,t . In the bipartite K2,2-free process, we begin with an empty graph on vertex set X ∪ Y, |X| = |Y | = n. At each step, a random edge from X × Y is added under the restriction that no K2,2 is formed. This step is repeated until no more edges can be added. In this note, we analyze this process and prove that the resulting graph shows that b(2, t) = Ω(t3/2/ log t), thereby improving the best known lower bound.

DOI

10.37236/9101

Published Citation

Bal, D., & Bennett, P. (2020). The Bipartite $K_{2,2}$-Free Process and Bipartite Ramsey Number $b(2, t)$. The Electronic Journal of Combinatorics, 27(4), #P4.23. https://doi.org/10.37236/9101

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