Superlinear subset partition graphs with dimension reduction, strong adjacency, and endpoint count

TL;DR

This paper constructs a sequence of subset partition graphs with specific properties that demonstrate a superlinear lower bound on diameter, providing evidence against the Linear Hirsch Conjecture.

Contribution

It introduces a new sequence of subset partition graphs with properties that challenge the Linear Hirsch Conjecture by exhibiting superlinear diameter growth.

Findings

Subset partition graphs can have superlinear diameter.

The constructed graphs satisfy key properties like dimension reduction and adjacency.

Results support the conjecture's limitations against linear bounds.

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.