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, 7142217899

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..19.

Gunnar Brinkmann, Jan Goedgebeur, Jonas Hägglund, and Klas Markström, Generation and properties of Snarks, arXiv:1206.6690 [math.CO], 2012-2013.

Jan Goedgebeur, Edita Máčajová, and Martin Škoviera, Smallest snarks with oddness 4 and cyclic connectivity 4 have order 44, arXiv:1712.07867 [math.CO], 2017-2019.

Gunnar Brinkmann and Steven Van Overberghe, Algorithms for the Generation of Snarks, arXiv:2603.17789 [math.CO].

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

a(19) using Brinkmann and Van Overberghe's data added by Andrei Zabolotskii, May 23 2026

Status

approved