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.

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