A Gr\"obner basis characterization for chordal comparability graphs
  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. 
Hidefumi Ohsugi and Takayuki Hibi
math.CO math.AC