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According to Tutte's five-flow conjecture, \\Phi_G(5) > 0 for any bridgeless G.A conjecture by Welsh that \\Phi_G(Q) has no real roots for Q \\in (4,\\infty) was recently disproved by Haggard, Pearce and Royle. These authors conjectured the absence of roots for Q \\in [5,\\infty). We study the real roots of \\Phi_G(Q) for a family of non-planar cubic graphs known as generalised Petersen graphs G(m,k). 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Jacobsen, Jesus Salas","submitted_at":"2010-09-21T11:19:23Z","abstract_excerpt":"The number of nowhere zero Z_Q flows on a graph G can be shown to be a polynomial in Q, defining the flow polynomial \\Phi_G(Q). According to Tutte's five-flow conjecture, \\Phi_G(5) > 0 for any bridgeless G.A conjecture by Welsh that \\Phi_G(Q) has no real roots for Q \\in (4,\\infty) was recently disproved by Haggard, Pearce and Royle. These authors conjectured the absence of roots for Q \\in [5,\\infty). We study the real roots of \\Phi_G(Q) for a family of non-planar cubic graphs known as generalised Petersen graphs G(m,k). 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