Classifications and characterizations of snarks

AbstractIn this paper vertex-reductions of snarks are considered. Each reduction naturally divides the class of snarks into three classes. The first class contains those snarks which are not reducible to a snark. The second contains those which are not reducible to a 3-colorable graph and the third one consists of the snarks which are reducible to a snark as well as to a 3-colorable graph.We distinguish three kinds of vertex-reductions according to the distance between the vertices used for the reduction. We give several characterizations of the induced classes, and we give structural characterizations in terms of 2-factors.We construct infinite families of snarks belonging to a certain class and analyze the relations between the classes