The h*-Polynomial of the Cut Polytope
of K2,m in the Lattice Spanned by its Vertices
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.
Full version: pdf,
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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