Edge connectivity of simplicial polytopes

We show that the graph of a simplicial polytope of dimen-sion d > 3 has no nontrivial minimum edge cut with fewer than d(d+1)/2 edges, hence the graph is min{& delta;, d(d+1)/2}-edge-connected where & delta; denotes the minimum degree. When d = 3, this implies that every minimum edge cut in a plane trian-gulation 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.& COPY; 2023 Elsevier Ltd. All rights reserved.