The construction and reduction of strong snarks Original Research Article

Let G be a 3-regular graph and let w be a weight function, w : E(G) → {1, 2}, for which the edges of weight 2 form a 1-factor of G. If w can be choosen such that there does not exist a circuit cover C for (G, w) in which each edge of G is contained in w(e) circuits of C then G is called a strong snark. Several methods are known for constructing snarks, and the reverse process has also been studied, see for example Cameron et al. (1987). We study the decomposition and construction of strong snarks.