On end degrees and infinite cycles in locally finite graphs
On end degrees and infinite cycles in locally finite graphs
复制标题
关于局部有限图中的结束度和无限循环
DOI：
10.1007/s00493-007-2149-0
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发表时间：
2007
期刊：
影响因子：
1.1
通讯作者：
M. Stein
中科院分区：
文献类型：
--
作者：
H. Bruhn;M. Stein
我们引入顶点度数到末端的自然扩展。对于 Diestel 和 Kühn [4, 5] 提出的允许无限循环的循环空间 C(G)，我们证明局部有限图的边集 G 位于 C(G) 中当且仅当每个顶点和每个端都有偶数度。以同样的方式，我们将有限图中的循环表征推广到局部有限图作为其 2-正则连通子图。
We introduce a natural extension of the vertex degree to ends. For the cycle spaceC(G) as proposed by Diestel and Kühn [4, 5], which allows for infinite cycles, we prove that the edge set of a locally finite graphGlies inC(G) if and only if every vertex and every end has even degree. In the same way we generalise to locally finite graphs the characterisation of the cycles in a finite graph as its 2-regular connected subgraphs.