TY - JOUR
T1 - On the log concavity of reliability and matroidal sequences
AU - Brown, Jason L.
AU - Colbourn, Charles J.
PY - 1994/3
Y1 - 1994/3
N2 - 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.
AB - 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.
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U2 - 10.1006/aama.1994.1004
DO - 10.1006/aama.1994.1004
M3 - Article
AN - SCOPUS:0348021601
SN - 0196-8858
VL - 15
SP - 114
EP - 127
JO - Advances in Applied Mathematics
JF - Advances in Applied Mathematics
IS - 1
ER -