On the log concavity of reliability and matroidal sequences

Jason L. Brown, Charles J. Colbourn

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)114-127
Number of pages14
JournalAdvances in Applied Mathematics
Volume15
Issue number1
DOIs
StatePublished - Mar 1994
Externally publishedYes

ASJC Scopus subject areas

  • Applied Mathematics

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