摘要: 设
![](https://image.hanspub.org/IMAGE/Edit_7dc8b0d4-15ca-4996-ae2c-7d0f5dc279a2.jpg)
及
![](https://image.hanspub.org/IMAGE/Edit_292da959-4a07-427a-a739-e1641fdec4ad.jpg)
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
![](https://image.hanspub.org/IMAGE/Edit_9346134c-0da8-40a8-920d-615958377a66.jpg)
且
Y中的顶点的度分别为
![](https://image.hanspub.org/IMAGE/Edit_397c3e19-3f59-4324-abac-cf5da0cf867d.jpg)
,那么称序列对
![](https://image.hanspub.org/IMAGE/Edit_838ff192-a023-43ef-a054-92752a9a34ab.jpg)
是二部可图的。如果
![](https://image.hanspub.org/IMAGE/Edit_838ff192-a023-43ef-a054-92752a9a34ab.jpg)
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
![](https://image.hanspub.org/IMAGE/Edit_838ff192-a023-43ef-a054-92752a9a34ab.jpg)
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
![](https://image.hanspub.org/IMAGE/Edit_7dc8b0d4-15ca-4996-ae2c-7d0f5dc279a2.jpg)
and
![](https://image.hanspub.org/IMAGE/Edit_292da959-4a07-427a-a739-e1641fdec4ad.jpg)
be two non-increasing sequences of nonnegative integers. The pair
![](https://image.hanspub.org/IMAGE/Edit_838ff192-a023-43ef-a054-92752a9a34ab.jpg)
is said to be bigraphic if there is a simple
X,Y-bigraph such that the vertices of
X have degrees
![](https://image.hanspub.org/IMAGE/Edit_9346134c-0da8-40a8-920d-615958377a66.jpg)
and the vertices of
Y have degrees
![](https://image.hanspub.org/IMAGE/Edit_292da959-4a07-427a-a739-e1641fdec4ad.jpg)
.
![](https://image.hanspub.org/IMAGE/Edit_838ff192-a023-43ef-a054-92752a9a34ab.jpg)
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
![](https://image.hanspub.org/IMAGE/Edit_838ff192-a023-43ef-a054-92752a9a34ab.jpg)
to be t-bigraphic. In fact, it is a gen-eration of the Gale-Ryser type characterization theorem.