Colloquium by Ander Lamaison (Freie Universität Berlin): Ramsey density of infinite paths

Dec 10, 2018 | 04:00 PM s.t.

In a two-colouring of the edges of the complete graph on the natural numbers, what is the densest monochromatic infinite path that we can always find? We measure the density of a path by the upper asymptotic density of its vertex set. This question was first studied by Erdös and Galvin, who proved that the best density is between 2/3 and 8/9. In this talk we settle this question by proving that we can always find a monochromatic path of upper density at least (12+sqrt(8))/17=0.87226…, and constructing a two-colouring in which no denser path exists. This represents joint work with Jan Corsten, Louis DeBiasio and Richard Lang.

Time & Location

Dec 10, 2018 | 04:00 PM s.t.

Freie Universität Berlin
Institut für Informatik
Takustr. 9
14195 Berlin
Room 005 (Ground Floor)

Freie Universität Berlin
Technische Universität Berlin
Humboldt-Universität zu Berlin
Deutsche Forschungsgemeinschaft (DFG)