A033995 Number of bipartite graphs with n nodes.

1, 1, 2, 3, 7, 13, 35, 88, 303, 1119, 5479, 32303, 251135, 2527712, 33985853, 611846940, 14864650924, 488222721992, 21712049275198, 1308300679611469, 106897965189674291, 11852113048215107822, 1784730721403509209215, 365323537513403184463273

Offset: 0

Author

Ronald C. Read

Keywords

• nonn
• nice

Comments

All bipartite graphs are perfect. - Falk Hüffner, Nov 27 2015

EULER transform of A005142 [1, 1, 1, 3, 5, 17, ...] is [1, 2, 3, 7, 13, ...]. - Michael Somos, May 13 2019

Examples

			For n=1: o; n=2: o o, o-o; n=3: o o o, o o-o, o-o-o; n=4: o o o o, o o o-o, o-o o-o, o o-o-o, o-o-o-o, K_{2,2}, K_{3,1}. - _Michael Somos_, May 13 2019
		

References

• R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50
• CombOS - Combinatorial Object Server, Generate graphs.
• P. Erdős, D. J. Kleitman, and B. L. Rothschild, Asymptotic enumeration of k_n-free graphs. In Colloquio Internazionale sulle Teorie Combinatorie, (Rome, 1973), Tomo II, Atti dei Convegni Lincei, No. 17, pp. 19-27. Accad. Naz. Lincei, Rome.
• P. Hanlon, The enumeration of bipartite graphs, Discrete Math. 28 (1979), 49-57.
• S. Hougardy, Home Page.
• S. Hougardy, Classes of perfect graphs, Discr. Math. 306 (2006), 2529-2571.
• Sage, Common Graphs (Graph Generators).
• Eric Weisstein's World of Mathematics, Bipartite Graph.
• Eric Weisstein's World of Mathematics, Bicolorable Graph.
• Eric Weisstein's World of Mathematics, n-Colorable Graph.

Crossrefs

Row sums of A297877.

The labeled version is A047864.

Equals A076278(n) + 1.

Cf. A005142 (connected).

Programs

Mathematica

A005142 = Cases[Import["https://oeis.org/A005142/b005142.txt", "Table"], {, }][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A005142] (* Jean-François Alcover, Mar 18 2020 *)

Extensions

a(0)=1 prepended and terms a(21) and beyond from Andrew Howroyd, Sep 05 2018