Edge Deletion-Contraction in the Chromatic and Tutte Symmetric Functions

Abstract: We consider symmetric function analogues of the chromatic and Tutte polynomials on graphs whose vertices have positive integer weights. We show that in this setting these functions admit edge deletion-contraction relations akin to those of the corresponding polynomials, and we use these relations to give enumerative and/or inductive proofs of properties of these functions. In particular we note that the Tutte symmetric function in this form is related to a family of vertex-weighted graph functions, from which we derive a recipe theorem and a spanning-tree expansion.

This is joint work with Sophie Spirkl.

combinatorics

Audience: researchers in the topic

York University Applied Algebra Seminar