Facets and facet subgraphs of symmetric edge polytopes

Chen, Tianran; Davis, Robert; Korchevskaia, Evgeniia

doi:10.1016/j.dam.2022.11.015

Cited by 6 publications

(2 citation statements)

References 15 publications

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“…Given a facet-defining function f as in Theorem 2.1, we write G f for the corresponding facet subgraph, i.e., the subgraph with vertex set V and edge set E f . Lemma 2.3 (Chen, Davis, Korchevskaia (6)). Let G be a connected graph.…”

Section: Facets Of G(n P)mentioning

confidence: 99%

“…Symmetric edge polytopes, also called type PV adjacency polytopes, have been the subject of extensive recent study (2,6,7,8,9,10,14,15,16,17,18,20,21,22). One problem of interest is to establish relationships between the combinatorial structure of G and geometric properties of P G , motivated by applications in both pure and applied contexts.…”

Section: Introductionmentioning

confidence: 99%

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Facets of Random Symmetric Edge Polytopes, Degree Sequences, and Clustering

Braun,

Bruegge,

Kahle

2023

Discrete Mathematics &Amp; Theoretical Computer Science

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Symmetric edge polytopes are lattice polytopes associated with finite simple graphs that are of interest in both theory and applications. We investigate the facet structure of symmetric edge polytopes for various models of random graphs. For an Erd\H{o}s-Renyi random graph, we identify a threshold probability at which with high probability the symmetric edge polytope shares many facet-supporting hyperplanes with that of a complete graph. We also investigate the relationship between the average local clustering, also known as the Watts-Strogatz clustering coefficient, and the number of facets for graphs with either a fixed number of edges or a fixed degree sequence. We use well-known Markov Chain Monte Carlo sampling methods to generate empirical evidence that for a fixed degree sequence, higher average local clustering in a connected graph corresponds to higher facet numbers in the associated symmetric edge polytope.

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Section: Facets Of G(n P)mentioning

confidence: 99%