Edge connectivity of simplicial polytopes

Abstract

We show that the graph of a simplicial polytope of dimension d≥3 has no nontrivial minimum edge cut with fewer than d(d+1)/2 edges, hence the graph is min{δ,d(d+1)/2}-edge-connected where δ denotes the minimum degree. When d=3, this implies that every minimum edge cut in a plane triangulation is trivial. When d≥4, we construct a simplicial d-polytope whose graph has a nontrivial minimum edge cut of cardinality d(d+1)/2, proving that the aforementioned result is best possible.