On 2-factors containing 1-factors in bipartite graphs
On 2-factors containing 1-factors in bipartite graphs
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关于二部图中包含 1 因子的 2 因子
DOI：
10.1016/s0012-365x(99)90061-4
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
M. Jacobson
中科院分区：
文献类型：
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作者：
Guantao Chen;R. Gould;M. Jacobson
Moon和Moser（Israel J.Math.1（1962）163-165）证明了：如果G是阶为2n且最小度为σ_n（n + 1）/2的平衡二部图，则G是Hamilton图。最近，证明了他们著名的度条件也意味着存在一个2-因子，恰好有k个循环，提供n max {52，2k 2 + 1}。在本文中，我们证明了一个相似度条件意味着对于每个完美匹配M，存在一个2-因子，它恰好有k个圈包含M的所有边。
Moon and Moser (Israel J. Math. 1 (1962) 163–165) showed that if G is a balanced bipartite graph of order 2n and minimum degree σ ⩾ (n + 1)/2, then G is hamiltonian. Recently, it was shown that their well-known degree condition also implies the existence of a 2-factor with exactly k cycles provided n ⩾ max {52, 2k2+ 1}. In this paper, we show that a similar degree condition implies that for each perfect matching M, there exists a 2-factor with exactly k cycles including all edges of M.