Welsh's conjecture on flow roots is false. In fact, many cubic graphs with reasonably large girth and enough vertices have flow roots between 4 and 5, and it is almost certain that we can find graphs with flow roots arbitrarily close to 5.
However I strongly believe that "All real roots of nonzero flow polynomials are at most FIVE".
See my recent survey article "Recent results on chromatic and flow roots of graphs and matroids, Surveys in Combinatorics 2009" for more detail.
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CSI of Charles University
Welsh's conjecture is false
Welsh's conjecture on flow roots is false. In fact, many cubic graphs with reasonably large girth and enough vertices have flow roots between 4 and 5, and it is almost certain that we can find graphs with flow roots arbitrarily close to 5.
However I strongly believe that "All real roots of nonzero flow polynomials are at most FIVE".
See my recent survey article "Recent results on chromatic and flow roots of graphs and matroids, Surveys in Combinatorics 2009" for more detail.
Gordon Royle