A130315 Number of nontrivial (girth >=5) snarks on 2n nodes.

0, 0, 0, 0, 1, 0, 0, 0, 2, 6, 20, 38, 280, 2900, 28399, 293059, 3833587, 60167732, 1051945967

Offset

1,9

Comments

Snarks are cyclically 4-edge connected cubic graphs with chromatic index 4 and girth >= 5.

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.

Gunnar Brinkmann, Jan Goedgebeur, Jonas Hägglund, and Klas Markström, Generation and properties of Snarks, J. Comb. Theory, Series B, 103 (4) (2013), 468-488.

Gunnar Brinkmann and Steven Van Overberghe, Algorithms for the Generation of Snarks, arXiv:2603.17789 [math.CO], 2026.

Jonas Hägglund and Klas Markström, On stable cycles and cycle double covers of graphs with large circumference, Discrete Math., 312 (2012), 2540-2544.

House of Graphs, Snarks

Eric Weisstein's World of Mathematics, Snark

Crossrefs

Cf. A216834.

Sequence in context: A218883 A353699 A202963 * A087150 A323724 A214307

Adjacent sequences: A130312 A130313 A130314 * A130316 A130317 A130318

Keyword

nonn,hard,more

Author

Eric W. Weisstein, May 22 2007

Extensions

a(15), a(16) added from Hagglund-Markstrom by N. J. A. Sloane, Jul 26 2012

a(17), a(18) added by Jan Goedgebeur, Jul 31 2012

a(19) from Brinkmann and Van Overberghe added by Andrei Zabolotskii, May 23 2026

Status

approved