Snarks and Reducibility

A snark is a simple, cyclically \(4\)-edge connected, cubic graph with girth at least \(5\) and chromatic index \(4\). We give a complete list of all snarks of order less than \(30\). Motivated by the long standing discussion on trivial snarks (i.e. snarks which are reducible), we also give a brief survey on different reduction methods for snarks. For all these reductions we give the complete numbers of irreducible snarks of order less than \(30\) and the number of nonisomorphic \(3\)-critical subgraphs of these graphs. The results are obtained with the aid of a computer.