Alladi Ramakrishnan Hall

On the characterization of chordal graphs using Horn hypergeometric series

R Venkatesh

IISc Bangalore

In [Radchenko & Villegas, Bull. Lond. Math. Soc., 2021], Radchenko and Villegas proved that a finite simple graph
G is chordal if and only if the inverse of the independence polynomial of G is Horn hypergeometric. In this talk,
we present a new proof of their result using some elementary combinatorial methods and also generalize their
result to POE graphs that could possibly have a countably infinite number of vertices. Our proof is based on the
connection between the independence polynomial of G with the multi-colored chromatic polynomials of G which was
established first in [Arunkumar, Kus, and Venkatesh, J. Algebra, 2018].