### Abstract

A graphical partition of the even integer n is a partition of n where each part of the partition is the degree of a vertex in a simple graph and the degree sum of the graph is n. In this note, we consider the problem of enumerating a subset of these partitions, known as graphical forest partitions, graphical partitions whose parts are the degrees of the vertices of forests (disjoint unions of trees). We shall prove that gf(2k) = p(0) + p(1) + p(2) + ... + p(k - 1) where gf(2k) is the number of graphical forest partitions of 2k and p(j) is the ordinary partition function which counts the number of integer partitions of j.

Original language | English (US) |
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Pages (from-to) | 33-37 |

Number of pages | 5 |

Journal | Ars Combinatoria |

Volume | 65 |

State | Published - Oct 1 2002 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Frank, D. A., Savage, C. D., & Sellers, J. A. (2002). On the Number of Graphical Forest Partitions.

*Ars Combinatoria*,*65*, 33-37.