Snarks and reducibility (Q2713660)

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 \(G'\). NEWLINENEWLINENEWLINEThe 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.