Recent developments in graph Ramsey theory
Recent developments in graph Ramsey theory
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DOI：
10.1017/cbo9781316106853.003
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发表时间：
2015-01
影响因子：
9.9
通讯作者：
D. Conlon;J. Fox;B. Sudakov
中科院分区：
文献类型：
--
作者：
D. Conlon;J. Fox;B. Sudakov
给定一个图$H$，Ramsey数$r(H)$是最小自然数$N$，使得$K_N$的边的任何双色包含$H$的一个单色副本。这些数字的存在早在1930年就已为人所知，但人们仍然不太清楚它们的数量行为。尽管如此，在极端组合数学的许多进展的推动下，拉姆齐数及其变体的研究最近取得了很大进展。在这项调查中，我们将描述其中的一些进展。
Given a graph $H$, the Ramsey number $r(H)$ is the smallest natural number $N$ such that any two-colouring of the edges of $K_N$ contains a monochromatic copy of $H$. The existence of these numbers has been known since 1930 but their quantitative behaviour is still not well understood. Even so, there has been a great deal of recent progress on the study of Ramsey numbers and their variants, spurred on by the many advances across extremal combinatorics. In this survey, we will describe some of this progress.