| 引用本文: | 杜彩凤. 立方图中的路因子和圈因子[J]. 科学技术与工程, 2010, (27): |
| Du caifeng. Path and cycle factors of cubic graphs[J]. Science Technology and Engineering, 2010, (27): |
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| 立方图中的路因子和圈因子 |
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杜彩凤1
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中国石油大学（华东）
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| 摘要: |
| 给定连通图集合 ，对图 的生成子图 ，如果 的每个分支都同构于集合 的一个元素，则 被称为 的 -因子。最近Kawarabayashi 等证明了：2-连通立方图有一个 -因子和 -因子，其中 表示阶为 的圈， 表示阶为 的路。Kano等给出了每一个阶至少为8的立方偶图有 -因子和 -因子的结论，并且提出猜想：阶至少为6的3-连通立方图有 -因子和 -因子。本文给出这个猜想的证明。 |
| 关键词: 路因子 圈因子 立方图 正则图 |
| DOI： |
| 分类号:0157.5 |
| 基金项目: |
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| Path and cycle factors of cubic graphs |
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Du caifeng
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| Abstract: |
| For a set of connected graphs, a spanning subgraph of a graph is called an -factor if every component of is isomorphic to a member of . It was recently shown by Kawarabayashi et al. that every 2-connected cubic graph has a -factor and -factor, where denote the cycle of order n and denote the path of order n. Kano et al. show that every connected cubic bipartite graph has a -factor and -factor if its order is at least 8. And they have conjectured that every 3-connected cubic graph of order at least six has a -factor. In this paper, we give a proof of this conjecture. |
| Key words: path factor cycle factor cubic graph regular graph |
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