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Deformation cones of graphical zonotopes for K4-free graph

2024/04/03 by Germain Poullot, Poullot, Germain
Mathematics · #05C20 #52B05 #52B11 #52B12 #Combinatorics (math.CO) #FOS: Mathematics #Morphological variations and asymmetry

paper · pdf · doi:10.48550/arxiv.2404.02669

openalex publication_date 2024/04/03 · openalex created_date 2024/04/06 · openalex updated_date 2026/08/02

Abstract

In this paper, we compute a triangulation of certain faces of the submodular cone. More precisely, graphical zonotopes are generalized permutahedra, and hence their deformation cones are faces of the submodular cone. We give a triangulation of these faces for graphs without induced complete sub-graph on 4 vertices. We deduce the rays of these faces: Minkowski indecomposable deformations of these graphical zonotopes are segments and triangles. Besides, computer experiments lead to examples of graphs without induced complete sub-graph on 5 vertices, whose graphical zonotopes have high dimensional Minkowski indecomposable deformations.

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