| k正则偶图对集矩阵的分解定理 |
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| 引用本文： | 滕桂兰.k正则偶图对集矩阵的分解定理[J].天津大学学报(自然科学与工程技术版),1997,30(5):631-635. |
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| 作者姓名： | 滕桂兰 |
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| 作者单位： | 天津大学成人教育学院 |
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| 摘 要： | 证明了一个ｎ阶非负实矩阵可分解为某些ｎ阶置换矩阵的线性组合的定理，由此得到了ｋ－正则偶图的对集矩阵的分解定理，这些定量衣其证明给出了ｋ－正则偶图的完美匹配的构造方法，并举例说明对集矩阵的分解不是唯一的。
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| 关 键 词： | k－正则偶图 对集矩阵 置换矩阵 完美匹配 |
DECOMPOSITION THEOREMS ON THE BIPARTITION MATRICES OF k REGULAR BIPARTITITE GRAPHS |
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| Teng Guilan.DECOMPOSITION THEOREMS ON THE BIPARTITION MATRICES OF k REGULAR BIPARTITITE GRAPHS[J].Journal of Tianjin University(Science and Technology),1997,30(5):631-635. |
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| Authors: | Teng Guilan |
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| Abstract: | In this paper we prove a theorem, which says that a nonnegative real matrix of order n can be decomposited into a linear combination of some permutation matrices of order n . It follows that decomposition theorems on the bipartition matrices of k regular bipartite graphs are obtained. These theorems and their proofs show a structural method for finding the perfect matchings of a k regular bipartite graph. We present an example to show that the decomposition of a bipartition matrix is not unique. |
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| Keywords: | k regular bipartite graph bipartition matrix permutation matrix perfect matching |
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