| P_(4k-1)-factorization of bipartite multigraphs |
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| 引用本文： | WANG Jian & DU Beiliang Nantong Vocational College,Nantong 226007,China, Department of Mathematics,Suzhou University,Suzhou 215006,China. P_(4k-1)-factorization of bipartite multigraphs[J]. 中国科学A辑(英文版), 2006, 0(7) |
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| 作者姓名： | WANG Jian & DU Beiliang Nantong Vocational College Nantong 226007 China Department of Mathematics Suzhou University Suzhou 215006 China |
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| 作者单位： | WANG Jian & DU Beiliang Nantong Vocational College，Nantong 226007，China; Department of Mathematics，Suzhou University，Suzhou 215006，China |
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| 摘 要： | LetλKm,n be a bipartite multigraph with two partite sets having m and n vertices, respectively. A Pν-factorization ofλKm,n is a set of edge-disjoint Pν-factors ofλKm,n which partition the set of edges ofλKm,n. Whenνis an even number, Ushio, Wang and the second author of the paper gave a necessary and sufficient condition for the existence of a Pν-factorization ofλKm,n. When v is an odd number, we proposed a conjecture. However, up to now we only know that the conjecture is true forν= 3. In this paper we will show that the conjecture is true whenν= 4k-1. That is, we shall prove that a necessary and sufficient condition for the existence of a P4k-1-factorization ofλKm,n is (1) (2k-1)m≤2kn, (2) (2k-1)n≤2km, (3)m n = 0 (mod 4k-1), (4)λ(4k-1)mn/[2(2k-1)(m n)] is an integer.
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P_(4k-1)-factorization of bipartite multigraphs |
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| WANG Jian , DU Beiliang Nantong Vocational College,Nantong ,China. P_(4k-1)-factorization of bipartite multigraphs[J]. Science in China(Mathematics), 2006, 0(7) |
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| Authors: | WANG Jian & DU Beiliang Nantong Vocational College Nantong China |
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| Affiliation: | WANG Jian & DU Beiliang Nantong Vocational College,Nantong 226007,China, Department of Mathematics,Suzhou University,Suzhou 215006,China |
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| Abstract: | |
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| Keywords: | bipartite multigraph factor factorization. |
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