Gr\"obner Bases and Nullstellens\"atze for Graph-Coloring Ideals
Symbolic Computation
2014-10-28 v1 Computational Complexity
Commutative Algebra
Algebraic Geometry
Combinatorics
Abstract
We revisit a well-known family of polynomial ideals encoding the problem of graph--colorability. Our paper describes how the inherent combinatorial structure of the ideals implies several interesting algebraic properties. Specifically, we provide lower bounds on the difficulty of computing Gr\"obner bases and Nullstellensatz certificates for the coloring ideals of general graphs. For chordal graphs, however, we explicitly describe a Gr\"obner basis for the coloring ideal, and provide a polynomial-time algorithm.
Cite
@article{arxiv.1410.6806,
title = {Gr\"obner Bases and Nullstellens\"atze for Graph-Coloring Ideals},
author = {Jesús A. De Loera and Susan Margulies and Michael Pernpeintner and Eric Riedl and David Rolnick and Gwen Spencer and Despina Stasi and Jon Swenson},
journal= {arXiv preprint arXiv:1410.6806},
year = {2014}
}
Comments
16 pages