Algebraic Graph Theory Seminar - Willem H. Haemers

Title: The chromatic index of strongly regular graphs (joint work with Sebastian M. Cioaba and Krystal Guo)

Abstract:

It follows from Vizing's theorem that the chromatic index (edge chromatic number) of a k-regular graph equals k or k+1, and that it equals k+1 if the graph has odd order.

We investigate the chromatic index of strongly regular graphs (SRGs) of even order.

It turns out that, except for the Petersen graph, all investigated connected SRGs of even order have chromatic index equal to the degree, and we conjecture that this is the case for all connected SRGs of even order.