2018/09/03 by Doolittle, Joseph
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1809.00662
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.