Brinkmann, G.; Steffen, E. Snarks and reducibility. (English) Zbl 0963.05050 Ars Comb. 50, 292-296 (1998). A snark is a simple, cyclically 4-edge connected cubic graph with girth at least 5 and chromatic index 4. A cubic graph \(G\) is vertex-reducible to a simple cubic graph \(G'\) if \(G'\) can be obtained from \(G\) by removing two vertices together with all incident edges from \(G\) and adding new edges to obtain \(G'\). The complete list of all snarks of order less than 30 is given. Moreover, a brief survey of different reduction methods for snarks is presented. For all these reductions the complete numbers of irreducible snarks of order less than 30 and the number of nonisomorphic 3-critical subgraphs of these graphs is given. Reviewer: Dalibor Fronček (Ostrava) Cited in 16 Documents MSC: 05C15 Coloring of graphs and hypergraphs 05C75 Structural characterization of families of graphs Keywords:snarks; vertex reducibility PDFBibTeX XMLCite \textit{G. Brinkmann} and \textit{E. Steffen}, Ars Comb. 50, 292--296 (1998; Zbl 0963.05050)