Consider an $n$-vertex graph $G$ whose edges are coloured with $s$ colours so that there is no monochromatic clique of size $k$, and call such a colouring of $G$ valid. The Erd\H{o}s-Rothschild problem from 1974 is to determine the maximum number of valid colourings over all $n$-vertex graphs $G$. This problem is in general wide open and an exact (or even asymptotic) answer is only known for a few pairs $(k,s)$. In this talk I will discuss a method for obtaining new exact results. Joint work with Oleg Pikhurko.
Due to the ongoing covid-19 epidemic, seminars are via Zoom. To receive the Zoom link, please contact the seminar organiser: Victor Falgas Ravry
