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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).


Barnes, T. M. and Savage, C. D. ``A Recurrence for Counting Graphical Partitions.'' Electronic J. Combinatorics 2, R11 1-10, 1995.

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.''

Sloane, N. J. A. Sequence A000569 in ``The On-Line Version of the Encyclopedia of Integer Sequences.''

© 1996-9 Eric W. Weisstein