Geodesic
A Recurrence for Counting Graphical Partitions
The electronic journal of combinatorics, Tome 2 (1995)
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In this paper, we give a recurrence to enumerate the set $G(n)$ of partitions of a positive even integer $n$ which are the degree sequences of simple graphs. The recurrence gives rise to an algorithm to compute the number of elements of $G(n)$ in time $O(n^4)$ using space $O(n^3)$. This appears to be the first method for computing $|G(n)|$ in time bounded by a polynomial in $n$, and it has enabled us to tabulate $|G(n)|$ for even $n \leq 220$. 
@article{10_37236_1205,
     author = {Tiffany M. Barnes and Carla D. Savage},
     title = {A {Recurrence} for {Counting} {Graphical} {Partitions}},
     journal = {The electronic journal of combinatorics},
     year = {1995},
     volume = {2},
     doi = {10.37236/1205},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1205/}
}
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%A Carla D. Savage
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Tiffany M. Barnes; Carla D. Savage. A Recurrence for Counting Graphical Partitions. The electronic journal of combinatorics, Tome 2 (1995). doi: 10.37236/1205

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