The polynomial method for list-colouring extendability of outerplanar graphs
Przemys{\l}aw Gordinowicz, Pawe{\l} Twardowski
TL;DR
This paper reformulates Hutchinson's theorems on list-colouring extendability of outerplanar graphs using graph polynomials, simplifying proofs and generalizing results through the polynomial method and Alon-Tarsi theory.
Contribution
It introduces a polynomial-based framework for analyzing list-colouring extendability, providing simplified proofs and broader applicability compared to previous combinatorial approaches.
Findings
Reformulation of Hutchinson's theorems using graph polynomials
Simplification of existing proofs through polynomial methods
Generalization of list-colouring extendability results
Abstract
We restate theorems of Hutchinson on list-colouring extendability for outerplanar graphs in terms of non-vanishing monomials in a graph polynomial, which yields an Alon-Tarsi equivalent for her work. This allows to simplify her proofs as well as obtain more general results.
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