PIMS - UVic Discrete Math Seminar: Tony Huynh

In 2017, Ron Aharoni proposed the following generalization of the Caccetta-Häggkvist conjecture: if G is a simple n-vertex edge-colored graph with n color classes of size at least r, then G contains a rainbow cycle of length at most the ceiling of n/r.

I will begin with a summary of recent progress on Aharoni's conjecture based on a new survey article of Katie Clinch, Jackson Goerner, Freddie Illingworth, and myself. I will then sketch a proof that Aharoni's conjecture holds up to an additive constant for each fixed r. The last result is joint work with Patrick Hompe.