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, Rödl and Szemerédi showed that for every \(n\ge 1\) there exists a graph \(G'\) on n vertices each of degree at most three, with 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 Rödl and Szemerédi’s construction leads to a bound \({\hat{r}}(G')\ge cn\,\exp (c\sqrt{\log n})\).

图\(G'\)的大小拉姆齐数\({\hat{r}}(G')\)被定义为最小整数m，因此存在一个具有m 个边的图G，使得每 2 – G边缘的着色包含\(G'\)的单色副本。回答 Beck、Rödl 和 Szemerédi 的问题表明，对于每个\(n\ge 1\)，都存在一个图\(G'\)，在n 个顶点上，每个顶点的度数最多为 3，且大小拉姆齐数至少为\( cn\log ^{\frac{1}{60}}n\)为通用常数\(c>0\)。在这篇文章中，我们证明对 Rödl 和 Szemerédi 构造的修改会导致有界\({\hat{r}}(G')\ge cn\,\exp (c\sqrt{\log n})\)。