It is shown that if pn → ∞, w.h.p., whenever G = G(n, p) is 2-edge-coloured there is a monochromatic path of length (2/3 + o(1))n, which is optimal in the sense that 2/3 cannot be replaced by a larger constant.Expand

This paper proves the conjecture that for every $2$-edge-colouring of G, the vertex set V(G) may be partitioned into two vertex-disjoint cycles, one of each colour.Expand

The k-colour bipartite Ramsey number of a bipartite graph H is the least integer n for which every k-edge-coloured complete bipartite graph Kn,n contains a monochromatic copy of H. The study of… Expand

It is proved that for every r-edge-colouring of Kn there is a monochromatic triple star of order at least n/r-1, improving Ruszinko's result 2012.Expand

It is proved that any H -free graph with minimum degree at least d contains an induced bipartite subgraph of minimum degreeAt least c H log d /log log d , thus nearly confirming one and proving another conjecture of Esperet, Kang and Thomassé.Expand

We show that every r-uniform hypergraph on n vertices which does not contain a tight cycle has at most O(n(logn)) edges. This is an improvement on the previously best-known bound, of ne √ , due to… Expand

This paper determines asymptotically the $4$-colour bipartite Ramsey number of paths and cycles which are close to being tight and provides new upper bounds on the $k$- Colour bipartites Ramsey numbers which are Close to being Tight.Expand