On maximal graphical partitions that are the nearest to a given graphical partition

On the Number of Graphical Forest Partitions

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 t...

Graphical Basis Partitions

A partition of an integer n is graphical if it is the degree sequence of a simple undirected graph It is an open question whether the fraction of partitions of n which are graphical approaches as n approaches in nity A partition is basic if the number of dots in its Ferrers graph is minimum among all partitions with the same rank vector as In this paper we investigate graphical partitions via b...

Dominance Order and Graphical Partitions

We gave a new criterion for graphical partitions. We derive a new recursion formula, which allows the computation of the number g(n) of graphical partitions of weight n for up to n > 900.

Eecient Generation of Graphical Partitions

Given a positive even integer n we show how to generate the set G n of graphical partitions of n that is those partitions of n which correspond to the degree sequences of simple undirected graphs The algorithm is based on a recurrence for G n and the total time used by the algorithm independent of output is O jG n j which is constant average time per graphical partition This is the rst algorith...

Graphical Abstracts