On Alternating 6-Cycles in Edge-Coloured Graphs

Abstract

In this short note, we use flag algebras to prove that the number of colour alternating $6$-cycles in a red/blue colouring of a large clique is asymptotically maximized by a uniformly random colouring. This settles the first open case of a problem of Basit, Granet, Horsley, Kündgen and Staden.