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arXiv · 1804.02451

Three-colour bipartite Ramsey number for graphs with small bandwidth

Guilherme Oliveira Mota
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Abstract

We estimate the $3$-colour bipartite Ramsey number for balanced bipartite graphs $H$ with small bandwidth and bounded maximum degree. More precisely, we show that the minimum value of $N$ such that in any $3$-edge colouring of $K_{N,N}$ there is a monochromatic copy of $H$ is at most $\big(3/2+o(1)\big)|V(H)|$. In particular, we determine asymptotically the $3$-colour bipartite Ramsey number for balanced grid graphs.

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Guilherme Oliveira Mota. 2018-04-06. Three-colour bipartite Ramsey number for graphs with small bandwidth. https://arxiv.org/abs/1804.02451

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