论文标题
无限图因子的拉姆西上部密度
Ramsey upper density of infinite graph factors
论文作者
论文摘要
ErdőS和Galvin在1993年启动了对Ramsey理论上的上层密度问题的研究。在本文中，我们关注以下问题：给定固定的有限图$ F $，$λ$的最大值是什么，以至于每2架2 edge the $ \ mathbb {n} $上的完整图中的每个2 edge the n} $ younter toct in y monsoter toct in y mathbb {n} $ fulloase $ f $ f $ - $λ$？ 在这里，我们证明了这个问题的新下限。对于$ f $的某些选择，包括集团和奇数周期，这种新的界限非常敏锐，因为它与较旧的上限相匹配。对于特定情况，$ f $是三角形，我们还给出了$ 1- \ frac {1} {\ sqrt {7}} = 0.62203 \ dots $的显式下限，改善了先前的3/5最佳界限。
The study of upper density problems on Ramsey theory was initiated by Erdős and Galvin in 1993. In this paper we are concerned with the following problem: given a fixed finite graph $F$, what is the largest value of $λ$ such that every 2-edge-coloring of the complete graph on $\mathbb{N}$ contains a monochromatic infinite $F$-factor whose vertex set has upper density at least $λ$? Here we prove a new lower bound for this problem. For some choices of $F$, including cliques and odd cycles, this new bound is sharp, as it matches an older upper bound. For the particular case where $F$ is a triangle, we also give an explicit lower bound of $1-\frac{1}{\sqrt{7}}=0.62203\dots$, improving the previous best bound of 3/5.
