Exact Ramsey numbers in multipartite graphs arising from Hadamard matrices and strongly regular graphs

In this paper we investigate bounds on set multipartite Ramsey numbers for the bipartite graph K2,n, extending or improving well-known upper bounds by Chung and Graham, Irving, Lortz and Mengersen. Known constructions based on certain classes of combinatorial designs (projective plane, Hadamard matrix, strongly regular graph) yield near-optimal bounds. As the main goal, a new construction based on strongly regular graph and Hadamard matrix produces a sharp class, generalizing a classical bound by Exoo, Harborth, and Mengersen.