On removable cycles through every edge
On removable cycles through every edge
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DOI：
10.1002/jgt.v42:2
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发表时间：
2003-02
影响因子：
0.9
通讯作者：
Manoel Lemos;J. Oxley
中科院分区：
文献类型：
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作者：
Manoel Lemos;J. Oxley
Mader和Jackson独立证明了每一个最小度至少为4的2连通简单图G都有一个可移动的环，即一个使G- e (C)为2连通的环C。研究了2连通图G的每条边，无论简单与否，何时能保证在某可移动循环内的问题。主要结果表明，如果从G中删除的每两条边都保持2连通，那么，不仅每条边都在一个可移动环中，而且对于每两条边，都存在不相交的可移动环，使得每条边都包含一条可区分的边。©2002 Wiley期刊公司[J] .图论学报（自然科学版），2009
Mader and Jackson independently proved that every 2-connected simple graph G with minimum degree at least four has a removable cycle, that is, a cycle C such that G-E(C) is 2-connected. This paper considers the problem of determining when every edge of a 2-connected graph G, simple or not, can be guaranteed to lie in some removable cycle. The main result establishes that if every deletion of two edges from G remains 2-connected, then, not only is every edge in a removable cycle but, for every two edges, there are edge-disjoint removable cycles such that each contains one of the distinguished edges. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 155–164, 2003