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].