Journal of Integer Sequences, Vol. 23 (2020), Article 20.7.5

The h*-Polynomial of the Cut Polytope of K2,m in the Lattice Spanned by its Vertices

Ryuichi Sakamoto
Department of Mathematical Sciences
Graduate School of Science and Technology
Kwansei Gakuin University
Sanda, Hyogo 669-1337


The cut polytope of a graph is an important object in several fields, such as functional analysis, combinatorial optimization, and probability. For example, Sturmfels and Sullivant showed that the toric ideals of cut polytopes are useful in algebraic statistics. In the theory of lattice polytopes, the h*-polynomial is an important invariant. However, except for trees, there are no classes of graphs for which the h*-polynomial of their cut polytope is explicitly specified. In the present paper, we determine the h*-polynomial of the cut polytope of the complete bipartite graph K2,m using the theory of Gröbner bases of toric ideals.

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Received June 12 2019; revised versions received July 5 2019; September 26 2019; September 28 2019; April 9 2020. Published in Journal of Integer Sequences, June 27 2020.

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