论文标题
多彩色拉姆齐数字中的塔间隙
Tower Gaps in Multicolour Ramsey Numbers
论文作者
论文摘要
解决了Conlon，Fox和Rödl的问题，我们在其2美元的$ -Colour和$ Q $ -COLOUR RAMSEY号码之间建立了一个任意塔高度分离的HyperGraphs家族。该结构的基础主要引理是Erdős的新变体 - Hajnal加强引理的通用ramsey Number $ r_k（t; q，p）$，我们将其定义为最小的整数$ n $，因此每个$ q $ q $ q $ q $ q $ n $ n $ n $ dertices co $ than $ than $ than $ than $ than $ than $ taste $ than $ than $ taste $ than $ tasten $ than $ taste $ tear caul caus ca $ tasten $ tears caul caul caus c $ tear caul cover的范围很少。我们的结果提供了这些数字上的第一个塔式下限。
Resolving a problem of Conlon, Fox, and Rödl, we construct a family of hypergraphs with arbitrarily large tower height separation between their $2$-colour and $q$-colour Ramsey numbers. The main lemma underlying this construction is a new variant of the Erdős--Hajnal stepping-up lemma for a generalized Ramsey number $r_k(t;q,p)$, which we define as the smallest integer $n$ such that every $q$-colouring of the $k$-sets on $n$ vertices contains a set of $t$ vertices spanning fewer than $p$ colours. Our results provide the first tower-type lower bounds on these numbers.
