Ramsey upper density of infinite graphs

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Ander Lamaison


Let H be an infinite graph. In a two-coloring of the edges of the complete graph on the natural numbers, what is the densest monochromatic subgraph isomorphic to H that we are guaranteed to find? We measure the density of a subgraph by the upper density of its vertex set. This question, in the particular case of the infinite path, was introduced by Erdős and Galvin. Following a recent result for the infinite path, we present bounds on the maximum density for other choices of H, including exact values for a wide class of bipartite graphs.

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Lamaison, A. (2019). Ramsey upper density of infinite graphs. Acta Mathematica Universitatis Comenianae, 88(3), 897-901. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1194/742