A Recurrence for Counting Graphical Partitions

Author:

Barnes Tiffany M.,Savage Carla D.

Abstract

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 $n \leq 220$.

Publisher

The Electronic Journal of Combinatorics

Subject

Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Asymptotic Bounds on Graphical Partitions and Partition Comparability;International Mathematics Research Notices;2020-10-06

2. Efficient counting of degree sequences;Discrete Mathematics;2019-03

3. Asymptotic joint distribution of the extremities of a random Young diagram and enumeration of graphical partitions;Advances in Mathematics;2018-05

4. Sufficient Conditions for Graphicality of Bidegree Sequences;SIAM Journal on Discrete Mathematics;2017-01

5. Mahonian pairs;Journal of Combinatorial Theory, Series A;2012-04

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