Algebraic Graph Theory Seminar - Thomás Spier

Title: Graph Continued Fractions

Abstract:

This talk is about a connection between matching polynomials and continued fractions. For the matching polynomials: we prove a refinement of a theorem by Ku and Wong, which extends the classical Gallai-Edmonds decomposition; we present a generalization of Sturm's classical theorem about the number of zeros of a real polynomial in an interval; we characterize the number of distinct zeros in terms of the dimension of a vector space generated by a family of matching polynomials; we prove an upper bound on the number of paths that start at some vertex of a graph.