Non-Stanley bounds for network reliability
type: Item
instance of: scholarly article
title: Non-Stanley bounds for network reliability
zbMATH Open document ID: 0846.05046
DOI: 10.1023/A:1022484229443
author: Jason I. Brown
author: Charles J. Colbourn
published in: Journal of Algebraic Combinatorics
publication date: 1996-03-17T00:00:00Z
review text: Let \(G\) be a connected graph with \(n\) vertices and \(m\) edges. If each edge is independently operational with probability \(p\) then the reliability of \(G\) is the probability that the operational edges form a spanning connected subgraph. This amount can be written as \[ p^{n- 1} \sum^{m- n+ 1}_{i= 0} H_i(1- p)^i \] and the (nonnegative integer) coefficients \(H_i\) form the \(H\)-vector. The authors prove new bounds for \(H\)-vectors and the results ``shed light on the problem of characterizing the \(H\)-vectors of matroids''.
reviewed by: András Recski
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 90B35
Mathematics Subject Classification ID: 94C15
zbMATH DE Number: 843618
zbMATH Keywords: network reliability
zbMATH Keywords: connected graph
zbMATH Keywords: probability
zbMATH Keywords: bounds
zbMATH Keywords: \(H\)-vectors
zbMATH Keywords: matroids
MaRDI profile type: Publication
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full work available at URL: a:1022484229443
OpenAlex ID: W2069741057
description: scientific article; zbMATH DE number 843618