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Algebra & Combinatorics Seminar

Title: A simple proof for the characterization of chordal graphs using Horn hypergeometric series
Speaker: R. Venkatesh (IISc Mathematics)
Date: 13 December 2023
Time: 11:30 am
Venue: LH-3, Mathematics Department

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.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 29 Feb 2024