The bipartite Ramsey numbers $BR(C_8, C_{2n})$

The bipartite Ramsey numbers $BR(C_8, C_{2n})$

For the given bipartite graphs $G_1,G_2,\ldots,G_t$, the multicolor bipartite Ramsey number $BR(G_1,G_2,\ldots,G_t)$ is the smallest positive integer $b$ such that any $t$-edge-coloring of $K_{b,b}$ contains a monochromatic subgraph isomorphic to $G_i$, colored with the $i$th color for some $1\leq i...

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Bibliographic Details
Main Authors: Mostafa Gholami, Yaser Rowshan
Format: Article
Language:English
Published: Discrete Mathematics & Theoretical Computer Science 2024-02-01
Series:Discrete Mathematics & Theoretical Computer Science
Subjects:
mathematics - combinatorics
Online Access:http://dmtcs.episciences.org/11207/pdf
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Summary:For the given bipartite graphs $G_1,G_2,\ldots,G_t$, the multicolor bipartite Ramsey number $BR(G_1,G_2,\ldots,G_t)$ is the smallest positive integer $b$ such that any $t$-edge-coloring of $K_{b,b}$ contains a monochromatic subgraph isomorphic to $G_i$, colored with the $i$th color for some $1\leq i\leq t$. We compute the exact values of the bipartite Ramsey numbers $BR(C_8,C_{2n})$ for $n\geq2$.
ISSN:1365-8050

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