The‐color bipartite Ramsey number of a bipartite graph is the least integer for which every‐
edge‐colored complete bipartite graph contains a monochromatic copy of. The study of …

Abstract Let R (C n) R\left (C _n\right) be the Ramsey number of the cycle on nn vertices. We
prove that, for some C> 0 C> 0, with high probability every 2‐coloring of the edges of G (N …

Abstract Let H 1,…, H k be bipartite graphs. The bipartite Ramsey number br (H 1,…, H k) is
the minimum integer N such that any k-edge-coloring of the complete bipartite graph KN, N …

For an integer r≥ 2 and bipartite graphs H i, where 1≤ i≤ r the bipartite Ramsey number br
(H 1, H 2,…, H r) is the minimum integer N such that any r-edge coloring of the complete …

We show that for any positive integer r there exists an integer k and a k-colouring of the
edges of K 2 k+ 1 with no monochromatic odd cycle of length less than r. This makes …

A Gallai coloring is a coloring of the edges of a complete graph without rainbow triangles,
and a Gallai k-coloring is a Gallai coloring that uses at most k colors. For an integer k≥ 1 …

For graphs G and H, let G⟶ k H signify that any k-edge coloring of G contains a
monochromatic H as a subgraph. Let G (K 2 (N), p) be random graph spaces with edge …

A connected matching in a graph GG is a matching contained in a connected component of
G G. A well‐known method due to Łuczak reduces problems about monochromatic paths …