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

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 K4. The univariate Brown–Colbourn conjecture is false for certain simple planar graphs obtained from K4 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.