The Brown-Colbourn conjecture on zeros of reliability polynomials is false

Gordon Royle, A.D. Sokal

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

We give counterexamples to the Brown-Colbourn conjecture on reliability polynomials, in both its univariate and multivariate forms. The multivariate Brown-Colbourn conjecture is false already for the complete graph K-4. The univariate Brown-Colbourn conjecture is false for certain simple planar graphs obtained from K-4 by parallel and series expansion of edges. We show, in fact, that a graph has the multivariate Brown-Colbourn property if and only if it is series-parallel. (C) 2004 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)345-360
JournalJournal of combinatorial Theory Series B
Volume91
Issue number2
DOIs
Publication statusPublished - 2004

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