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

Vol.05 No.01(2016), Article ID:17015,3 pages
10.12677/AAM.2016.51016

A Generalization of the Gale-Ryser Type Characterization Theorem

Jiyun Guo, Dongmei Wang

College of Information Science and Technology, Hainan University, Hainan Haikou

Received: Feb. 4th, 2016; accepted: Feb. 19th, 2016; published: Feb. 26th, 2016

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 generation of the Gale-Ryser type characterization theorem.

Keywords:Degree, Bigraphic Sequence, t-Bigraphic Sequence

Gale-Ryser型刻划定理的一个推广

1. 引言

(1)

2. 定理2的证明

A Generalization of the Gale-Ryser Type Characterization Theorem[J]. 应用数学进展, 2016, 05(01): 121-123. http://dx.doi.org/10.12677/AAM.2016.51016

1. 1. Gale, D. (1957) A Theorem on Flows in Networks. Pacific Journal of Mathematics, 7, 1073-1082. http://dx.doi.org/10.2140/pjm.1957.7.1073

2. 2. Ryser, H.J. (1957) Combinatorial Properties of Matrices of Zeros and Ones. Canada Journal of Mathematics, 9, 371-377. http://dx.doi.org/10.4153/CJM-1957-044-3