Odd Ramsey numbers of multipartite graphs and hypergraphs
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912501373861888 |
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| author | Crawford, Nicholas Heath, Emily Henderschedt, Owen Schwieder, Coy Zerbib, Shira |
| author_facet | Crawford, Nicholas Heath, Emily Henderschedt, Owen Schwieder, Coy Zerbib, Shira |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19456 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Odd Ramsey numbers of multipartite graphs and hypergraphs Crawford, Nicholas Heath, Emily Henderschedt, Owen Schwieder, Coy Zerbib, Shira Combinatorics 05D10, 05C55, 05C15 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. |
| title | Odd Ramsey numbers of multipartite graphs and hypergraphs |
| topic | Combinatorics 05D10, 05C55, 05C15 |
| url | https://arxiv.org/abs/2507.19456 |