Snark designs

Abstract

The main aim of this paper is to solve the design spectrum problem for Tietze's graph, the two 18-vertex Blanusa snarks, the six snarks on 20 vertices (including the flower snark J5), the twenty non- trivial snarks on 22 vertices (including the two Loupekine snarks) and Goldberg's snark #3. Together with the Petersen graph (for which the spectrum has already been computed) this list includes all non- trivial snarks of up to 22 vertices. We also give partial results for a selection of larger graphs: the two Celmins-Swart snarks, the 26- and 34-vertex Blanusa snarks, the flower snark 37, the double star snark, Zamfirescu's graph, Goldberg's snark #5, the Szekeres snark and the Watkins snark. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.