A130315 -id:A130315 - cp's OEIS frontend

A214327 Number of nontrivial (triangle-free and girth >=5) stable snarks on 2n nodes.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 7, 25, 228, 1456

Offset: 1

N. J. A. Sloane, Jul 26 2012

J. Hagglund and K. Markstrom, On stable cycles and cycle double covers of graphs with large circumference, Discrete Math., 312 (2012), 2540-2544.
Eric Weisstein's World of Mathematics, Snark

Cf. A130315.

A216834 Number of weak snarks on 2n nodes.

Original entry on oeis.org

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

Offset: 1

Jan Goedgebeur, Sep 19 2012

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.

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

Cf. A130315.

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

cp's OEIS Frontend

A214327 Number of nontrivial (triangle-free and girth >=5) stable snarks on 2n nodes.

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