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math.CO2026
Generalized Chromatic Polynomials of Cycles and uni-cyclic Graphs
Dipnit Biswas, R. Venkatesh
In \cite{R81}, Read obtained an explicit formula for the generalized chromatic polynomials of cycle graphs using the classical deletion-contraction principle. In this paper, we tak…
math.CO2025
On the Polytope Model and Near End node Isomorphisms of Type Kirillov--Reshetikhin Crystals
Dipnit Biswas, Irfan Habib
We prove an inductive formula to construct a path from the highest weight element to any given vertex in the crystal graph of the polytope realization of the Kirillov-Reshetikhin c…
math.CO2024
On the characterization of chordal graphs using Horn hypergeometric series
Dipnit Biswas, Irfan Habib, R. Venkatesh
Radchenko and Villegas characterized the chordal graphs by the inverse of their independence polynomials being Horn hypergeometric series in Radchenko et al. in 2021. In this paper…