应用数学进展  >> Vol. 5 No. 1 (February 2016)

Gale-Ryser型刻划定理的一个推广
A Generalization of the Gale-Ryser Type Characterization Theorem

DOI: 10.12677/AAM.2016.51016, PDF, HTML, XML, 下载: 1,431  浏览: 2,444  科研立项经费支持

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. Gale-Ryser型刻划定理的一个推广[J]. 应用数学进展, 2016, 5(1): 121-123. http://dx.doi.org/10.12677/AAM.2016.51016