A Gr\"obner basis characterization for chordal comparability graphs
Combinatorics
2018-09-03 v2 Commutative Algebra
Abstract
In this paper, we study toric ideals associated with multichains of posets. It is shown that the comparability graph of a poset is chordal if and only if there exists a quadratic Gr\"obner basis of the toric ideal of the poset. Strong perfect elimination orderings of strongly chordal graphs play an important role.
Cite
@article{arxiv.1602.00285,
title = {A Gr\"obner basis characterization for chordal comparability graphs},
author = {Hidefumi Ohsugi and Takayuki Hibi},
journal= {arXiv preprint arXiv:1602.00285},
year = {2018}
}
Comments
8 pages, Proposition 1.3 (normality) is added