On bicritical snarks
Eckhard Steffen · Czech digital mathematics library · 2001
Bicritical snarks are the irreducible ones with respect to the reductions considered by Nedela and Skoviera in [7]. We give a natural characterization of bicritical snarks and we characterize the elementary extensions of a snark. This solves Problem No. 6 of [7], and yields a method to construct all snarks starting from the irreducible ones. Then we show that for some n 10 and for each even n 92 there is a bicritical snark of order n. This solves Problem No. 5 of [7]. 1 Introduction We are using standard graph theoretical terminology and notation in this paper. We define a snark to be a cubic graph with chromatic index Ø 0 = 4. There are two main questions which lead to the study of reduction of snarks. The first one is the question about the intrinsic properties of cubic graphs which force them being a snark. The hope is that these properties can be detected in the irreducible snarks, and, since every snark is reducible to an irreducible one every snark should have this property...