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arXiv · 2507.19456

Odd Ramsey numbers of multipartite graphs and hypergraphs

Nicholas Crawford·Emily Heath·Owen Henderschedt·Coy Schwieder·Shira Zerbib
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Abstract

Given a hypergraph $G$ and a subhypergraph $H$ of $G$, the \emph{odd Ramsey number} $r_{odd}(G,H)$ is the minimum number of colors needed to edge-color $G$ so that every copy of $H$ intersects some color class in an odd number of edges. Generalizing a result of \cite{BHZ} in two different ways, in this paper we prove $r_{odd} \left(K_{n,n}, K_{2,t} \right)=\frac{n}{t} + o(n)$ for all $t\geq 2$, and $r_{odd} \left(\mathcal{K}^{(k)}_{n,\dots,n}, \mathcal{K}_{1,\dots,1,2,2} \right) = \frac{n}{2} + o(n)$ for all $k\geq 2$. The latter is the first result studying odd Ramsey numbers for hypergraphs.

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Nicholas Crawford, Emily Heath, Owen Henderschedt, Coy Schwieder, Shira Zerbib. 2025-07-25. Odd Ramsey numbers of multipartite graphs and hypergraphs. https://arxiv.org/abs/2507.19456

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