A126750 Number of 2-connected (or biconnected) graphs on n nodes with chromatic number 2.

0, 0, 0, 1, 1, 5, 8, 42, 146, 956, 6643, 65921, 818448, 13442572, 287665498, 8099980771, 300760170216, 14791653463768, 967055338887805, 84368806391412395, 9855854129239183783, 1546801291978378704267

Offset: 1

Author

N. J. A. Sloane, Feb 18 2007, Oct 01 2008

Keywords

• nonn

Comments

Equally, number of 2-connected (or biconnected) bipartite graphs on n nodes.

Also number of biconnected triangle-free graphs on n nodes with chromatic number 2, since chromatic number 2 implies triangle-free. - Gordon Royle, Apr 11 2007

See the Gainer-Dewar/Gessel reference for formulas and Sage code. - Ralf Stephan, May 18 2013

Links

• Keith M. Briggs, Combinatorial Graph Theory
• C. J. Colbourn and C. Huybrechts, Fully gated graphs,: recognition and convex operations, Discrete Math., 308 (2008), 5184-5195.
• A. Gainer-Dewar and I. M. Gessel, Enumeration of bipartite graphs and bipartite blocks, arXiv:1304.0139 [math.CO], 2013-2014.

Crossrefs

A diagonal of triangle in A126749.