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Superlinear Subset Partition Graphs With Dimension Reduction, Strong Adjacency, and Endpoint Count

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Abstract

We construct a sequence of subset partition graphs satisfying the dimension reduction, adjacency, strong adjacency, and endpoint count properties whose diameter has a superlinear asymptotic lower bound. These abstractions of polytope graphs give further evidence against the Linear Hirsch Conjecture.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de los Andes, Carrera Primera # 18A-12, Bogotá, D.C., Colombia

    Tristram C. Bogart

  2. Department of Mathematics, University of Wisconsin-La Crosse, 1725 State Street, La Crosse, WI, 54601, USA

    Edward D. Kim

Authors
  1. Tristram C. Bogart
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  2. Edward D. Kim
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Correspondence to Edward D. Kim.

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Bogart, T.C., Kim, E.D. Superlinear Subset Partition Graphs With Dimension Reduction, Strong Adjacency, and Endpoint Count. Combinatorica 38, 75–114 (2018). https://doi.org/10.1007/s00493-016-3327-8

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  • DOI: https://doi.org/10.1007/s00493-016-3327-8

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