A minimal counterexample to a strengthening of Perles' conjecture
Combinatorics
2018-09-10 v2
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.
Keywords
Cite
@article{arxiv.1809.00662,
title = {A minimal counterexample to a strengthening of Perles' conjecture},
author = {Joseph Doolittle},
journal= {arXiv preprint arXiv:1809.00662},
year = {2018}
}
Comments
8 pages, update to fix the coordinates in the example, and other minor changes