9 papers
A matroidal criterion for flow polytopes to be order polytopes
Akihiro Higashitani, Hidefumi Ohsugi
Flow polytopes of directed acyclic graphs form a central class of lattice polytopes in algebraic, geometric, and enumerative combinatorics. Order polytopes are one of the best unde…
Simplex faces and quadratic toric ideals of lattice polytopes
Aki Mori, Hidefumi Ohsugi
We say that a convex polytope has the clique-face property if every clique in its 1-skeleton is the vertex set of a face. We establish this property as a geometric necessary condit…
Algebraic aspects of unconditional lattice polytopes
Kenta Mori, Ryo Motomura, Hidefumi Ohsugi +1
Unconditional polytopes are convex polytopes that are symmetric with respect to all coordinate hyperplanes and arise naturally from anti-blocking polytopes by reflection. This pape…
On the Ehrhart Theory of Generalized Symmetric Edge Polytopes
Robert Davis, Akihiro Higashitani, Hidefumi Ohsugi
The symmetric edge polytope (SEP) of a (finite, undirected) graph is a centrally symmetric lattice polytope whose vertices are defined by the edges of the graph. SEPs have been stu…
Kempe equivalence and quadratic toric rings
Hidefumi Ohsugi, Akiyoshi Tsuchiya
Kempe equivalence is a classical and fundamental notion in graph coloring theory. In the present paper we establish a connection between Kempe equivalence and quadratic stable set…
Toric ideal of matching polytopes and edge colorings
Kenta Mori, Ryo Motomura, Hidefumi Ohsugi +1
In the present paper, we investigate the maximal degree of minimal generators of the toric ideal of the matching polytope of a graph. It is known that the toric ideal associated to…