Graphs and Matroids Seminar - Thomas Lesgourgues

Title: Ramsey with purple edges

Abstract: Motivated by a question of David Angell, we study a variant of Ramsey numbers where some edges are coloured with both red and blue colours, (i.e. are called ‘purple’ edges). Specifically, we are interested in the largest number g = g(s, t, n), for some s and t and n < R(s, t), such that there exists a red-blue-purple colouring of Kn with g purple edges, without a red-purple Ks and without a blue-purple Kt. We determine g asymptotically for a large family of parameters. The talk will be introductory in nature. Since the concept of double-coloured edges is new in this context, there is a plethora of open questions. Joint work with Anita Liebenau and Nye Taylor.