Year: 2026
Type: preprint
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 $(k-1)m+1\le km$. This settles a problem of Erdős, Faudree, Rousseau and Schelp, which is listed as problem 34 in the graph theory collection.
Source: arXiv (Cornell University)
Authors: Cambie, Stijn, Freschi, Andrea
Institutions: KU Leuven, HUN-REN Alfréd Rényi Institute of Mathematics
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7164183349
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