dorsal/arxiv
View SchemaRamsey number of a cycle versus a graph of a given size
| Authors | Stijn Cambie, Andrea Freschi, Patryk Morawski, Kalina Petrova, Alexey Pokrovskiy |
|---|---|
| Categories | |
| ArXiv ID | 2601.10238vv1 |
| URL | https://arxiv.org/abs/2601.10238 |
| License | http://creativecommons.org/licenses/by/4.0/ |
Abstract
In this paper, we prove that for every $k$ and every graph $H$ with $m$ edges and no isolated vertices, the Ramsey number $R(C_k,H)$ is at most $2m+\lfloor \frac{k-1}{2} \rfloor$, provided $m$ is sufficiently large with respect to $k$. This settles a problem of Erd\H{o}s, Faudree, Rousseau and Schelp.
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"abstract": "In this paper, we prove that for every $k$ and every graph $H$ with $m$ edges and no isolated vertices, the Ramsey number $R(C_k,H)$ is at most $2m+\\lfloor \\frac{k-1}{2} \\rfloor$, provided $m$ is sufficiently large with respect to $k$. This settles a problem of Erd\\H{o}s, Faudree, Rousseau and Schelp.",
"arxiv_id": "2601.10238",
"authors": [
"Stijn Cambie",
"Andrea Freschi",
"Patryk Morawski",
"Kalina Petrova",
"Alexey Pokrovskiy"
],
"categories": [
"math.CO"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "Ramsey number of a cycle versus a graph of a given size",
"url": "https://arxiv.org/abs/2601.10238",
"version": "v1"
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