Discrepancy and large dense monochromatic subsets
Discrepancy and large dense monochromatic subsets
复制标题
差异和大而密集的单色子集
作者：
Ross J. Kang;V. Patel;Guus Regts
ErdH{o}s和Pach（1983）引入了Ramsey数的基于自然度的推广，其中我们不是在$2$边的彩色完全图中寻找大的单色团，而是寻找高最小度或平均度的单色子图。在这里，我们以几种方式扩展了这些所谓的拟拉姆齐数的研究，特别是多色和均匀超图。
ErdH{o}s and Pach (1983) introduced the natural degree-based generalisations of Ramsey numbers, where instead of seeking large monochromatic cliques in a $2$-edge coloured complete graph, we seek monochromatic subgraphs of high minimum or average degree. Here we expand the study of these so-called quasi-Ramsey numbers in a few ways, in particular, to multiple colours and to uniform hypergraphs.
Quasi-Ramsey numbers are known to exhibit a certain unique phase transition and we show that this is also the case across the settings we consider. Our results depend on a density-biased notion of hypergraph discrepancy optimised over sets of bounded size, which may be of independent interest.
完整子图
影响因子：
0.9
作者：
Falgas-Ravry, Victor;Markström, Klas;Verstraëte, Jacques
通讯作者：
Verstraëte, Jacques