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Discrete Math

Ramsey upper density of infinite graphs

Ander Lamaison (Freie Universit├Ąt Berlin)

Location:  Hill 705
Date & time: Monday, 10 February 2020 at 2:00PM - 3:00PM

Abstract:

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 Erd?s 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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