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Number of weak snarks on 2n nodes.
0

%I #35 Feb 16 2025 08:33:18

%S 0,0,0,0,1,0,0,0,2,6,31,155,1297,12517,139854,1764950,25286953,

%T 404899916

%N Number of weak snarks on 2n nodes.

%C Multiple definitions of snarks exist which vary in strength. Here snarks are cyclically 4-edge connected cubic graphs with chromatic index 4. These are sometimes called weak snarks. Some stronger definitions require snarks to have girth >= 5 or to be cyclically 5-edge connected.

%H G. Brinkmann, J. Goedgebeur, J. Hagglund, and K. Markstrom, <a href="http://arxiv.org/abs/1206.6690">Generation and properties of Snarks</a>, arxiv 1206.6690 [math.CO], 2012-2013.

%H J. Goedgebeur, E. Máčajová and M. Škoviera, <a href="https://arxiv.org/abs/1712.07867">Smallest snarks with oddness 4 and cyclic connectivity 4 have order 44</a>, arXiv:1712.07867 [math.CO], 2017-2019.

%H House of Graphs, <a href="https://houseofgraphs.org/meta-directory/snarks">Snarks</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WeakSnark.html">Weak Snark</a>

%Y Cf. A130315.

%K nonn,hard,more,changed

%O 1,9

%A _Jan Goedgebeur_, Sep 19 2012

%E a(18) added by _Jan Goedgebeur_, May 31 2018