Corrine Yap, Rutgers University

Abstract

In this talk, we'll see many examples of why trees are a nice class of graphs to work with through the lens of matchings. We'll discuss some new extremal results about "almost-perfect" matchings in trees and applications to the so-called Hosoya index aka monomer-dimer partition function aka (unsigned) matching polynomial. This is based on joint work with Stijn Cambie, Bradley McCoy, Gunjan Sharma, and Stephan Wagner.