Ramsey Numbers in Kneser Graphs
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866915610423721984 |
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| author | Heath, Emily McCourt, Grace Parker, Alex Schwieder, Coy Zerbib, Shira |
| author_facet | Heath, Emily McCourt, Grace Parker, Alex Schwieder, Coy Zerbib, Shira |
| contents | We define the $r\textit{-Kneser Ramsey number}$ $R^{\textrm{KG}}_{r}(s, t)$ as the minimum integer $n$ such that every red/blue edge-coloring of the Kneser graph $\textrm{KG}(n,r)$ contains a red $s$-clique or a blue $t$-clique. We obtain general bounds on the numbers $R^{\textrm{KG}}_{r}(s, t)$, and make progress on two related Ramsey-type problems, one raised by Holmsen, Hrusak, and Roldán-Pensado, and the other posted by Pálvölgyi. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25734 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ramsey Numbers in Kneser Graphs Heath, Emily McCourt, Grace Parker, Alex Schwieder, Coy Zerbib, Shira Combinatorics We define the $r\textit{-Kneser Ramsey number}$ $R^{\textrm{KG}}_{r}(s, t)$ as the minimum integer $n$ such that every red/blue edge-coloring of the Kneser graph $\textrm{KG}(n,r)$ contains a red $s$-clique or a blue $t$-clique. We obtain general bounds on the numbers $R^{\textrm{KG}}_{r}(s, t)$, and make progress on two related Ramsey-type problems, one raised by Holmsen, Hrusak, and Roldán-Pensado, and the other posted by Pálvölgyi. |
| title | Ramsey Numbers in Kneser Graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2510.25734 |