一类(0,1)矩阵变换图的Hamilton性HAMILTONICITY OF INTERCHANGE GRAPHSOF A TYPE OF MATRICES OF ZEROS AND ONES
张和平
摘要(Abstract):
设G(R,S)表示m×n阶(0,1)矩阵类(R,S)的变换图.Brualdi提出问题:“G(R,S)有Hamilton圈吗?”当min{m,n}=2时,文献[3]中证明了此变换图是Hamilton连通的,并且是泛圈的(除K_1,K_2外),从而给该问题一个肯定的答案,当min{m,n}=3时,本文进一步地证明了此变换图是边Hamilton的(除K_1,K_2外),从而也给出该问题一个肯定的答案。
关键词(KeyWords): (0,1)矩阵;变换图;图的Hamilton性
基金项目(Foundation):
作者(Author): 张和平
参考文献(References):
- 1 Brualdi R A. Matrices of Zeros and ones with fixed row and column sum vectors. Linear Algebra and Appl, 1980; 33: 159~231
- 2 Brualdi R A, Li Qiao. Small diameter interchange graphs of classes of matriecs of zeros and ones. Linear Algebra and Appl, 1982;46: 177~184
- 3 张福基,张云浒,一类(0,1) 多面体.新疆大学学报,1990;7(4) :1~4
- 4 Zhang Fuji, Li Xueliang. Hamiltonicity of a type of interchange graphs. to appear in Discrete Math.
- 5 Welsh D J A. Matroid. Acadmic Press, London (1976) 10
- 6 Bondy J A and Murty U S R. Graph theory with applications. Macmillan, London and Elsevier, New York, 1976
- 7 李乔.矩阵论八讲.上海科学技术出版社,1988;124~138