The reliability of a graph G is the probability that G is connected, given that edges are independently operational with probability p. This is known to be a polynomial in p, and various sequences associated with this polynomial have been conjectured to be unimodal and indeed, log concave. We show that for any graph G, there is a subdivision for which the log concavity conjectures all hold. Further, we provide evidence for the well-known conjecture of the log concavity of the independent set numbers of a matroid.
ASJC Scopus subject areas
- Applied Mathematics