A sequence D=(d1, d2, ..., dn) of positive integers is graphic if it is the degree sequence of a simple graph, called in this case a {\em realization} of D. In this paper, we introduce the operation of 2-reduction, that subtracts 1 from two integers of D such that the resulting sequence D' is graphic if and only if D is graphic. We show that 2-reductions allow us to simply generate all the realizations of D, to prove existing characterizations of graphic sequences, as well as to propose new characterizations that highlight connections between mathematical and algorithmic aspects of graphic sequences.

翻译：一个由正整数组成的序列D=(d1, d2, ..., dn) 被称为图形序列，当它是某个简单图的度序列时，该简单图称为D的一个实现。在本文中，我们引入了2-约简操作，该操作从D的两个整数中各减去1，使得所得序列D'为图形序列当且仅当D为图形序列。我们证明了2-约简操作能够简化地生成D的所有实现，证明现有的图形序列特征刻画，并提出了新的特征刻画，这些刻画凸显了图形序列在数学与算法方面的内在联系。