Abstract
The edge polytope of a finite graph is the convex hull of the column vectors of its vertex-edge incidence matrix. In this paper, we discuss the existence of a regular unimodular triangulation of normal edge polytopes of finite graphs. For normal edge polytopes of finite graphs with d vertices, n edges, and no regular unimodular triangulations, we determine the polytope that has the following: (1) the smallest number of vertices (d = 9), (2) the smallest number of edges (n = 15), and (3) the smallest codimension (n − d = 4 andd = 17).
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Hamano, G. et al. (2017). The Smallest Normal Edge Polytopes with No Regular Unimodular Triangulations. In: Conca, A., Gubeladze, J., Römer, T. (eds) Homological and Computational Methods in Commutative Algebra. Springer INdAM Series, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-319-61943-9_10
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DOI: https://doi.org/10.1007/978-3-319-61943-9_10
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