The r-size-Ramsey number of a graph H is the smallest number of edges a graph G can have such that for every edge-coloring of G with r colors there exists a monochromatic copy of H in G. For a graph H, we denote by H^q the graph obtained from H by subdividing its edges with q − 1 vertices each. In a recent paper of Kohayakawa, Retter and Rödl, it is shown that for all constant integers q, r ≥ 2 and every graph H on n vertices and of bounded maximum degree, the r-size-Ramsey number of H^q is at most , for n large enough. We improve upon this result using a significantly shorter argument by showing that for any such graph H.

中文翻译：

---

短细分的大小-拉姆齐数

所述ř -size-Ramsey数的曲线图的ħ是边缘的最小数量的图ģ可以有这样，对于每一个边染色的ģ与ř颜色存在的单色副本ħ在ģ。对于图H，我们用H ^q表示通过将其边细分为q  − 1 个顶点而从H获得的图。在 Kohayakawa、Retter 和 Rödl 最近的一篇论文中，表明对于所有常数整数q，  r  ≥ 2 和n上的每个图H顶点和有界最大度数，对于n足够大，H ^q的r -size-Ramsey 数至多为。我们通过显示任何这样的图H使用明显更短的参数来改进这个结果。