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

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dc.creatorRoyle, Gordon
dc.creatorSokal, Alan D.
dc.date2003-01-19
dc.date2004-06-02
dc.date.accessioned2026-07-07T04:54:32Z
dc.date.available2026-07-07T04:54:32Z
dc.descriptionWe 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.
dc.descriptionLaTeX2e, 17 pages. Version 2 makes a few small improvements in the exposition. To appear in Journal of Combinatorial Theory B
dc.identifierhttps://arxiv.org/abs/math/0301199
dc.identifierhttp://arxiv.org/abs/math/0301199
dc.identifierJ. Combin. Theory B 91, 345-360 (2004)
dc.identifierdoi:10.1016/j.jctb.2004.03.008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66289
dc.subjectCombinatorics
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.subject05C99 (Primary) 05C40, 68M10, 68M15, 68R10, 82B20, 90B15, 90B18, 90B25, 94C15 (Secondary)
dc.titleThe Brown-Colbourn conjecture on zeros of reliability polynomials is false
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