Inflection points of reliability polynomials are dense in [0, 1]

Suppose we have a graph G (finite and undirected) where the vertices of G are always operational, but the edges of G operate independently with probability p ∈ [0, 1]. The all-terminal reliability of a graph G is the probability that every pair of vertices in G is connected by a path: that is, some spanning tree is operational. We prove that the points of inflections of all-terminal reliability polynomials are dense in [0,1]. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 67(4), 266–269 2016