A Gr\"obner basis characterization for chordal comparability graphs
Hidefumi Ohsugi, Takayuki Hibi
TL;DR
This paper establishes a connection between the chordality of comparability graphs of posets and the existence of quadratic Gr"obner bases for their associated toric ideals, linking graph theory and algebraic geometry.
Contribution
It provides a characterization of chordal comparability graphs via Gr"obner bases of toric ideals, bridging combinatorics and algebraic methods.
Findings
Chordal comparability graphs correspond to quadratic Gr"obner bases.
Strongly chordal graphs have important role in the characterization.
The paper offers an algebraic criterion for graph chordality.
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.
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