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

1,9

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

Table of n, a(n) for n=1..18.

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.

Sequence in context: A232171 A231816 A058028 * A287592 A054141 A007710

Adjacent sequences: A216831 A216832 A216833 * A216835 A216836 A216837

Keyword

nonn,hard,more

Author

Jan Goedgebeur, Sep 19 2012

Extensions

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

Status

approved