摘要: 设
及
是两个由非负整数构成的不增序列。如果存在一个简单
X，Y-二部图使得
X中的顶点的度分别为
且
Y中的顶点的度分别为
，那么称序列对
是二部可图的。如果
二部可图且任何两个来自不同部集的顶点之间最多连有t条边，那么称
是t-二部可图的。本文给出一个t-二部可图序列的刻划定理。事实上，该定理是Gale-Ryser型刻划定理的一个推广。
Abstract:
Let
and
be two non-increasing sequences of nonnegative integers. The pair
is said to be bigraphic if there is a simple
X,Y-bigraph such that the vertices of
X have degrees
and the vertices of
Y have degrees
.
is said to be t-bigraphic if it is bigraphic and no two vertices from different partite sets are joined by more than t edges. In this paper, we give a characterization for
to be t-bigraphic. In fact, it is a gen-eration of the Gale-Ryser type characterization theorem.