Upper bounds for ordered Ramsey numbers of forests and bounded-degree graphs

Lior Gishboliner; Xiangyu Li

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arXiv · 2609.38828

Upper bounds for ordered Ramsey numbers of forests and bounded-degree graphs

Lior Gishboliner·Xiangyu Li

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Abstract

We prove the following two upper bounds for ordered Ramsey numbers: (1) Every ordered forest $F$ on $n$ vertices satisfies $R_{<}(F,F)=O(n^{1+\lceil\logχ_{<}(F)\rceil})$. This in particular answers a question of Geneson, Holmes, Liu, Neidinger, Pehova and Wass. (2) There is a function $f$ such that, for every fixed ordered graph $H$ with maximum degree at most $Δ$ and interval chromatic number at most $k$, it holds that $R_{<}(H,K_n)=O_H(n^{f(Δ,k)})$.

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Lior Gishboliner, Xiangyu Li. 2026-09-30. Upper bounds for ordered Ramsey numbers of forests and bounded-degree graphs. https://arxiv.org/abs/2609.38828

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