度序列的约化准则
Reduced Criteria for Degree Sequences
摘要：
对于许多类型的图，已经发现了给出整数序列是这样的图的度序列的充要条件的准则。这些准则往往采取一组不等式的形式，在Erdens-Gallai准则（用于简单无向图）和Gale-Ryser准则（用于二部图）的情况下，已经表明，必须检查的不等式的数量可以显着减少。我们发现，类似的减少持有的相应标准，许多其他类型的图，包括二部r-多重图，二部图与结构边，有向图，r-多重图，和比赛。我们还证明了减少不平衡序列。
英文摘要：
For many types of graphs, criteria have been discovered that give necessary and sufficient conditions for an integer sequence to be the degree sequence of such a graph. These criteria tend to take the form of a set of inequalities, and in the case of the Erdős-Gallai criterion (for simple undirected graphs) and the Gale-Ryser criterion (for bipartite graphs), it has been shown that the number of inequalities that must be checked can be reduced significantly. We show that similar reductions hold for the corresponding criteria for many other types of graphs, including bipartite r-multigraphs, bipartite graphs with structural edges, directed graphs, r-multigraphs, and tournaments. We also prove a reduction for imbalance sequences.
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