Non-Stanley bounds for network reliability

Jason I. Brown, Charles J. Colbourn

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


Suppose that each edge of a connected graph G of order n is independently operational with probability p; the reliability of G is the probability that the operational edges form a spanning connected subgraph. A useful expansion of the reliability is as pn-1i=0d Hi(1 - p)i, and the Ball-Provan method for bounding reliability relies on Stanley's combinatorial bounds for the H-vectors of shellable complexes. We prove some new bounds here for the H-vectors arising from graphs, and the results here shed light on the problem of characterizing the H-vectors of matroids.

Original languageEnglish (US)
Pages (from-to)13-36
Number of pages24
JournalJournal of Algebraic Combinatorics
Issue number1
StatePublished - 1996
Externally publishedYes


  • Graph polynomial
  • H-vector
  • Matroid
  • Network reliability
  • Shellable complex

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics


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