On the number of colorings of a snark minus an edge

For a given snark G and a given edge e of G, let ψ(G, e) denote the nonnegative integer such that for a cubic graph conformal to G – {e}, the number of Tait colorings with three given colors is 18 · ψ(G, e). If two snarks G₁ and G₂ are combined in certain well‐known simple ways to form a snark G, there are some connections between ψ (G₁, e₁), ψ (G₂, e₂), and ψ(G, e) for appropriate edges e₁, e₂, and e of G₁, G₂, and G. As a consequence, if j and k are each a nonnegative integer, then there exists a snark G with an edge e such that ψ(G, e) = 2^j · 3^k. © 2005 Wiley Periodicals, Inc.