Year: 2026
Type: preprint
Abstract: The induced Ramsey number $r_{\mathrm{ind}}(G,H)$ is defined as the minimum order of a graph $F$ such that any 2-coloring of its edges with red and blue leads to either a red induced copy of $G$ or a blue induced copy of $H$. In 1998, Kohayakawa, Prömel, and Rödl conjectured that for any fixed graph $G$, there exists a constant $f=f(G)$ such that the induced Ramsey number $r_{\mathrm{ind}}(G, H)$ is bounded by $|V(H)|^f$ for every graph $H$. In this paper, we completely solve the Kohayakawa--Prömel--Rödl conjecture, which states that for any graphs $G$ and $H$ with $|V(G)|=k\ge2$ and $|V(H)|=t\ge2$, $r_{\mathrm{ind}}(G,H)\le t^{60k^2+3}$. This verifies the conjecture with $f(G)=60|V(G)|^2+3$.
Source: arXiv (Cornell University)
Authors: Zhong, Chuang, Kashima, Masaki, Mao, Yaping
Institutions: Qinghai Normal University, Keio University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: 拉姆齐理论和加莱-拉姆齐数及其应用研究, G8902729962
OpenAlex ID: W7223105125