A216834 Number of weak snarks on 2n nodes.

0, 0, 0, 0, 1, 0, 0, 0, 2, 6, 31, 155, 1297, 12517, 139854, 1764950, 25286953, 404899916

Offset: 1

Author

Jan Goedgebeur, Sep 19 2012

Keywords

• nonn
• hard
• more

Comments

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.

Links

• G. Brinkmann, J. Goedgebeur, J. Hagglund, and K. Markstrom, Generation and properties of Snarks, arxiv 1206.6690 [math.CO], 2012-2013.
• J. Goedgebeur, E. Máčajová and M. Škoviera, Smallest snarks with oddness 4 and cyclic connectivity 4 have order 44, arXiv:1712.07867 [math.CO], 2017-2019.
• House of Graphs, Snarks
• Eric Weisstein's World of Mathematics, Weak Snark

Crossrefs

Cf. A130315.

Extensions

a(18) added by Jan Goedgebeur, May 31 2018