Equitably colourable cycle decompositions

A -colouring of a decomposition of a graph is an assignment of colours to the vertices of . A colouring is equitable if each colour is represented (as closely as possible) an equal number of times on each block, i.e. for any two colours and , the number of vertices of colour and in any given block differ by at most 1. In this talk, we give an overview of colourings of designs and cycle decompositions, and present some recent joint results with Francesca Merola on the existence of equitably 2-colourable cycle decompositions of the cocktail party graph. In particular, we give a complete existence result for equitably 2-colourable -cycle decompositions of in various cases, including that or (mod ); is a power of 2; for a prime power; or .

The Atlantic Graph Theory Seminar series will take place every Wednesday from 3:30-4:30 ADT online via zoom. The talks, provided by researchers, postdocs and graduate students, will be on a variety of current topics in graph theory. If you would like to give a talk or attend, please email one of the organizers (Jason Brown and Danielle Cox).