Tutte Colloquium - Angèle Hamel

Title: Chromatic Symmetric Functions and H-Free Graphs

Abstract:

Chromatic symmetric functions are defined in terms of colourings of particular graphs. Some key conjectures in this area concern whether chromatic symmetric functions of claw-free graphs can be written in terms of other symmetric functions with positive coefficients.  Here we extend the claw-free idea to consider the e-positivity question for chromatic symmetric functions of H-free graphs with H ={claw, F},  where  F is a four-vertex graph.  We settle the question for all cases except H={claw, co-diamond}, and we provide some partial results in that case. This is joint work with Chinh Hoang and Jake Tuero.