Algebraic Graph Theory Seminar - Chris Godsil

Title: The Matchings Polynomial

Abstract:

A $k$-matching in a graph is a matching of size $k$, and $p(X,k)$ denotes the number of $k$-matchings in $X$.

The matching polynomial of a graph is a form of generating function for the sequence $(p(X,k))_{k\ge0}$.

If is closely related to the characteristic polynomial of a graph. I will discuss some of the many interesting properties of this polynomial, and some of the related open problems.