Graphical Partition

A graphical partition of order $n$ is the Degree Sequence of a Graph with $n/2$ Edges and no isolated Vertices. For $n=2$, 4, 6, ..., the number of graphical partitions is 1, 2, 5, 9, 17, ... (Sloane's A000569).

References

Barnes, T. M. and Savage, C. D. ``A Recurrence for Counting Graphical Partitions.'' Electronic J. Combinatorics 2, R11 1-10, 1995. http://www.combinatorics.org/Volume_2/volume2.html#R11.

Barnes, T. M. and Savage, C. D. ``Efficient Generation of Graphical Partitions.'' Disc. Appl. Math. 78, 17-26, 1997.

Ruskey, F. ``Information on Graphical Partitions.'' http://sue.csc.uvic.ca/~cos/inf/nump/GraphicalPartition.html.

Sloane, N. J. A. Sequence A000569 in ``The On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.