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Halfspace Representations of Path Polytopes of Trees

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arxiv 2502.21204 v1 pith:2BRCZ3NJ submitted 2025-02-28 math.CO math.STstat.TH

Amer Goel , Aida Maraj , Alvaro Ribot This is my paper · ORCID
classification math.COmath.STstat.TH
keywords polytopesgeometryhalfspacepathalgebraicapplicationsariseconstruction
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abstract

Given a tree $T$, its path polytope is the convex hull of the edge indicator vectors for the paths between any two distinct leaves in $T$. These polytopes arise naturally in polyhedral geometry and applications, such as phylogenetics, tropical geometry, and algebraic statistics. We provide a minimal halfspace representation of these polytopes. The construction is made inductively using toric fiber products.

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Cited by 1 Pith paper

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  1. Extended formulations for induced tree and path polytopes of chordal graphs

    cs.DM 2025-12 conditional novelty 7.0 of 10

    Induced tree and path polytopes of chordal graphs admit compact extended formulations and both families of incidence vectors form Hilbert bases.

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