Subgraph polytopes and independence polytopes of count matroids

Michele Conforti, Volker Kaibel, Matthias Walter*, Stefan Weltge

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    7 Citations (Scopus)

    Abstract

    Given a graph, the non-empty subgraph polytope is the convex hull of the characteristic vectors of all pairs (F,S) where S is a non-empty subset of nodes and F is a subset of the edges with both endnodes in S. We obtain a strong relationship between non-empty subgraph polytopes and spanning forest polytopes relating their extension complexities. We further show that these polytopes provide polynomial size extended formulations for independence polytopes of count matroids, generalizing recent results on sparsity matroids.

    Original languageEnglish
    Article number5968
    Pages (from-to)457-460
    Number of pages4
    JournalOperations research letters
    Volume43
    Issue number5
    DOIs
    Publication statusPublished - 14 Jul 2015

    Keywords

    • Count matroids
    • Extension complexity
    • Spanning tree polytope

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