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Seminar: New Bounds on Generalized Ramsey Numbers

Date
March 11, 2020
Time
11:00 a.m. - 12:00 p.m. ET
Location
ENG 210
Open To
All faculty, staff, students and guests are welcome to attend.

A (p,q)-colouring of a graph G is an edge-colouring of G (not necessarily proper) in which each p-clique contains edges of at least q distinct colours. We denote by f(n,p,q) the minimum number of colours needed for a (p,q)-coloring of the complete graph Kn. Note that determining all values of f(n,p,2) is equivalent to determining all diagonal Ramsey numbers. As such, finding good bounds on these (p,q)-colouring numbers is quite difficult in general. Indeed, the best upper and lower bounds on f(n,p,p) for all p are still those given by Erdos and Gyarfas in 1997. In this talk, I will give an overview of this problem and describe recent improvements on the probabilistic upper bound of Erdos and Gyarfas for several small cases of p.