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 G 1 and G 2 are combined in certain well‐known simple ways to form a snark G , there are some connections between ψ ( G 1 , e 1 ), ψ ( G 2 , e 2 ), and ψ( G , e ) for appropriate edges e 1 , e 2 , and e of G 1 , G 2 , 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.