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

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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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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Mathematics Subject Classification (2000)

  • 05B40
  • 05C12
  • 52B05
  • 90C05