Chennai Mathematical Institute

Seminars




Mathematics Seminar
Date: Friday, 1 December 2023
Time: 11 AM - 12 PM
Venue: Lecture Hall 1
A simple proof for the characterization of chordal graphs using Horn hypergeometric series

R. Venkatesh
IISc, Bengaluru.
01-12-23


Abstract

Let G be a finite simple graph (with no loops and no multiple edges), and let I_G(x) be the multi-variate independence polynomial of G. In 2021, Radchenko and Villegas proved the following interesting characterization of chordal graphs, namely G is chordal if and only if the power series I_G(x)^-1 is Horn hypergeometric. In this talk, I will give a simpler proof of this fact by computing I_G(x)^-1 explicitly using multi-coloring chromatic polynomials. This is a joint work with Dipnit Biswas and Irfan Habib