Locally seeded embeddings, and Ramsey numbers of bipartite graphs with sublinear bandwidth

Dylan J. Altschuler, Han Huang, Konstantin Tikhomirov

A seminal result of Lee asserts that the Ramsey number of any bipartite $d$-degenerate graph $H$ satisfies $\log r(H)=\log n+O(d)$. In particular, this bound applies to every b…