Spanning even subgraphs of 3‐edge‐connected graphs
Spanning even subgraphs of 3‐edge‐connected graphs
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DOI：
10.1002/jgt.20386
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发表时间：
2009-09
影响因子：
0.9
通讯作者：
B. Jackson;Kiyoshi Yoshimoto
中科院分区：
文献类型：
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作者：
B. Jackson;Kiyoshi Yoshimoto
根据Petersen定理，无桥三次图有一个2因子。H. Fleischner将这一结果推广到最小次至少为3的无桥图，证明了每一个无桥图都有一个生成偶子图。我们的主要结果是，在更强的3边连通性假设下，我们可以找到一个生成偶子图，其中每个分量至少有5个顶点。我们通过构造一个无限族的3边连通图来证明这在某种意义上是最佳可能的，其中每个生成偶子图都有一个5环作为分量。©2009 Wiley期刊公司[J] .图论学报（自然科学版），2009
By Petersen's theorem, a bridgeless cubic graph has a 2‐factor. H. Fleischner extended this result to bridgeless graphs of minimum degree at least three by showing that every such graph has a spanning even subgraph. Our main result is that, under the stronger hypothesis of 3‐edge‐connectivity, we can find a spanning even subgraph in which every component has at least five vertices. We show that this is in some sense best possible by constructing an infinite family of 3‐edge‐connected graphs in which every spanning even subgraph has a 5‐cycle as a component. © 2009 Wiley Periodicals, Inc. J Graph Theory 62: 37–47, 2009