Non-Stanley bounds for network reliability

Jason I. Brown; Charles J. Colbourn

doi:10.1023/a:1022484229443

Non-Stanley bounds for network reliability

Jason I. Brown, Charles J. Colbourn

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

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 p^n-1∑_i=0^d H_i(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 language	English (US)
Pages (from-to)	13-36
Number of pages	24
Journal	Journal of Algebraic Combinatorics
Volume	5
Issue number	1
DOIs	https://doi.org/10.1023/a:1022484229443
State	Published - 1996
Externally published	Yes

Keywords

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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AB - 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-1∑i=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.

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KW - Shellable complex

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Non-Stanley bounds for network reliability

Abstract

Keywords

ASJC Scopus subject areas

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