Ramsey number of a cycle versus a graph of a given size
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908767711395840 |
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| author | Cambie, Stijn Freschi, Andrea Morawski, Patryk Petrova, Kalina Pokrovskiy, Alexey |
| author_facet | Cambie, Stijn Freschi, Andrea Morawski, Patryk Petrova, Kalina Pokrovskiy, Alexey |
| contents | 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 Erdős, Faudree, Rousseau and Schelp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10238 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ramsey number of a cycle versus a graph of a given size Cambie, Stijn Freschi, Andrea Morawski, Patryk Petrova, Kalina Pokrovskiy, Alexey Combinatorics 05D10 (Primary) 05C38 (Secondary) 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 Erdős, Faudree, Rousseau and Schelp. |
| title | Ramsey number of a cycle versus a graph of a given size |
| topic | Combinatorics 05D10 (Primary) 05C38 (Secondary) |
| url | https://arxiv.org/abs/2601.10238 |