A deletion–contraction relation for the chromatic symmetric function. (October 2020) - Crew, Logan; Spirkl, Sophie
Abstract: We extend the definition of the chromatic symmetric function X G to include graphs G with a vertex-weight function w : V ( G ) → N . We show how this provides the chromatic symmetric function with a natural deletion–contraction relation analogous to that of the chromatic polynomial. Using this relation we derive new properties of the chromatic symmetric function, and we give alternate proofs of many fundamental properties of X G .