非对角Ramsey多重性中的图兰染色
组合数学
2024-01-31 v2
摘要
图 的\emph{Ramsey多重性常数}是当 趋于无穷时， 的 -边染色中单色有标副本 的最小密度的极限。Fox与Wigderson近期确定了一大类图，其Ramsey多重性常数由“图兰染色”序列达到；即其中一类颜色类构成平衡完全多部图边集的染色。他们家族中每个图取自取一个带关键边的连通不可3-染色图并添加许多悬挂边。我们将该结果推广至Ramsey多重性常数的一种非对角变体，其涉及最小化一个图的红色副本与另一个图的蓝色副本的加权和。
引用
@article{arxiv.2309.06959,
title = {Tur\'an Colourings in Off-Diagonal Ramsey Multiplicity},
author = {Joseph Hyde and Jae-baek Lee and Jonathan A. Noel},
journal= {arXiv preprint arXiv:2309.06959},
year = {2024}
}
备注
33 pages. Note that the first arXiv version of this paper contained several Ramsey multiplicity results for pairs of small graphs proved via the flag algebra method. We have decided to remove those results to make the paper shorter and more focused. We are currently preparing a second manuscript in which we plan to include generalizations of some of the statements that we removed