A Generalization of the Gale-Ryser Type Characterization Theorem

作者: 郭纪云 , 王冬梅 :海南大学信息科学技术学院,海南 海口;

关键词: 二部可图序列t-二部可图序列Degree Bigraphic Sequence t-Bigraphic Sequence

摘要: 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.

文章引用: 郭纪云 , 王冬梅 (2016) Gale-Ryser型刻划定理的一个推广。 应用数学进展, 5, 121-123. doi: 10.12677/AAM.2016.51016


[1] Gale, D. (1957) A Theorem on Flows in Networks. Pacific Journal of Mathematics, 7, 1073-1082.

[2] Ryser, H.J. (1957) Combinatorial Properties of Matrices of Zeros and Ones. Canada Journal of Mathematics, 9, 371-377.