Keywords:
Gröbner basis, Zero dimensional ideal, $S$-packing colorings, Shape's lemma
Abstract
In this paper, polynomial ideal theory is used to deal with the problem of the $S$-packing coloring of a finite undirected and unweighted graph by introducing a family of polynomials encoding the problem. A method to find the $S$-packing colorings of the graph is presented and illustrated by examples.