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arXiv · 1809.00662

A minimal counterexample to a strengthening of Perles' conjecture

Joseph Doolittle
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Abstract

In this paper, we present a minimal counterexample to a conjecture of Perles that answers a question of Haase and Ziegler. The example is a simple 4-polytope that has an induced 3-connected 3-regular subgraph, whose graph complement is connected. This subgraph is planar and not the graph of a facet of the polytope.

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Joseph Doolittle. 2018-09-06. A minimal counterexample to a strengthening of Perles' conjecture. https://arxiv.org/abs/1809.00662

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