AI 中文总结
本文给出了多色有序拉姆齐数的一般上界，基于区间色数和退化度，扩展了先前结果，并证明对有序匹配几乎紧。
AI 中文摘要
我们针对有序图的区间色数和退化度，给出了多色有序拉姆齐数的一个一般上界。我们扩展了Conlon、Fox、Lee和Sudakov（2017）的先前结果，证明了对于每个具有退化度$d\geq2$和区间色数$χ$的$n$顶点有序图$G^<$，其$q$色有序拉姆齐数满足$r_<(G^<;q) \in n^{O(d^{q-1}\lceil \logχ\rceil^{q-1})}$，对每个$q \geq 2$成立。对于固定参数$q,d,χ$，所得估计是$n$的多项式。对于无三角形有序图$G^<$，我们还提供了更强的估计$n^{O(q^2d {\lceil \log χ\rceil}^{q-1})}$。此外，根据Li（2026）最近的结果，我们的上界对于有序匹配几乎是紧的。
英文摘要
We provide a general upper bound on multicolor ordered Ramsey numbers in terms of the interval chromatic number and the degeneracy of an ordered graph. We extend previous results by Conlon, Fox, Lee, and Sudakov (2017) by showing that for every $n$-vertex ordered graph $G^<$ with degeneracy $d\geq2$, and interval chromatic number $χ$, its $q$-color ordered Ramsey number satisfies $r_<(G^<;q) \in n^{O(d^{q-1}\lceil \logχ\rceil^{q-1})}$ for every $q \geq 2$. For fixed parameters $q,d,χ$, the resulting estimate is polynomial in $n$. For triangle-free ordered graphs $G^<$, we also provide the stronger estimate $n^{O(q^2d {\lceil \log χ\rceil}^{q-1})}$. It also follows from a recent result by Li (2026) that our upper bound is almost tight for ordered matchings.
Comments22 pages
