2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66289We 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.LaTeX2e, 17 pages. Version 2 makes a few small improvements in the exposition. To appear in Journal of Combinatorial Theory BCombinatoricsStatistical MechanicsMathematical Physics05C99 (Primary) 05C40, 68M10, 68M15, 68R10, 82B20, 90B15, 90B18, 90B25, 94C15 (Secondary)text