论文标题
在有限的图形上，尺寸较大
On bounded degree graphs with large size-Ramsey numbers
论文作者
论文摘要
图$ g'$的尺寸 - ramsey number $ \ hat r（g'）$定义为最小的整数$ m $，因此存在一个图$ g $，带有$ m $ $ edges，因此每$ 2 $ cole $ g $的边缘包含$ g'$ $ g'$的单色副本。 Rodl和Szemeredi回答贝克的一个问题，表明，每$ n \ geq 1 $，每个$ n $顶点上的图$ g'$最多最多三个，其中尺寸 - ramsey编号至少$ cn \ log^{\ frac {\ frac {1}} {60} {60}} n $ for Universal Constant constants $ constants $ c constants $ c> 0 $ c> 0 $ c> 0 $ c> 0 $ c> 0。在本说明中，我们表明Rodl和Szemeredi的构造的修改会导致$ \ hat r（g'）\ geq cn \，\ exp（c \ sqrt {\ log n}）$。
The size-Ramsey number $\hat r(G')$ of a graph $G'$ is defined as the smallest integer $m$ so that there exists a graph $G$ with $m$ edges such that every $2$-coloring of the edges of $G$ contains a monochromatic copy of $G'$. Answering a question of Beck, Rodl and Szemeredi showed that for every $n\geq 1$ there exists a graph $G'$ on $n$ vertices each of degree at most three, with the size-Ramsey number at least $cn\log^{\frac{1}{60}}n$ for a universal constant $c>0$. In this note we show that a modification of Rodl and Szemeredi's construction leads to a bound $\hat r(G')\geq cn\,\exp(c\sqrt{\log n})$.
