The size-Ramsey number of a graph F is the smallest number of edges in a graph G with the Ramsey property for F, that is, with the property that any 2-colouring of the edges of G contains a monochromatic copy of F. We prove that the size-Ramsey number of the grid graph on n × n vertices is bounded from above by n3+o(1).

中文翻译：

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关于网格图的 size-Ramsey 数

图的大小-拉姆齐数F是图中的最小边数G与拉姆齐财产F，也就是说，具有任何 2 着色边缘的属性G包含的单色副本F. 我们证明了网格图的 size-Ramsey 数n×n顶点的边界为n3+o(1).