Automatic Generation of Generating Functions for Chromatic Polynomials for Grid Graphs (and more general creatures) of Fixed (but arbitrary!) Width

TL;DR

This paper presents a computer-assisted method to automatically derive rational generating functions for chromatic polynomials of grid graphs and similar structures using the transfer-matrix approach, advancing combinatorial graph theory.

Contribution

It introduces an automated approach to generate generating functions for chromatic polynomials of infinite graph sequences, generalizing previous manual methods.

Findings

Successfully derived rational generating functions for grid graphs

Automated transfer-matrix method applied to complex graph classes

Demonstrated the approach's rigor and generality

Abstract

This short article, dedicated to our beloved guru Philippe FLAJOLET (1948-2011), is a case-study in computer-generated combinatorial research, where the computer, all by itself, is using the transfer-matrix method to derive (rigorously!) rational generating functions for chromatic polynomials for infinite sequences of graphs generalizing the action of taking the Cartesian product with a path of length n, n=1,2,... .