| Cycles Containing a Subset of a Given Set of Elements in Cubic Graphs |
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| 作者姓名： | 宝升 |
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| 作者单位： | School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa; Institute of Discrete Mathematics, Inner Mongolia University of Nationalities, Inner Mongolia $028005$, P. R. China |
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| 基金项目： | 国家自然科学基金 (Grant No.10971027). |
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| 摘 要： | The technique of contractions and the known results in the study of cycles in $3$-connected cubic graphs are applied to obtain the following result. Let $G$ be a $3$-connected cubic graph, $X\subseteq V(G)$ with $|X| = 16$ and $e\in E(G)$. Then either for every $8$-subset $A$ of $X$, $A\cup\{e\}$ is cyclable or for some $14$-subset $A$ of $X$, $A\cup\{e\}$ is cyclable.
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| 关 键 词： | contraction cubic graphs cyclability. |
| 收稿时间： | 2012/6/12 0:00:00 |
| 修稿时间： | 2012/9/12 0:00:00 |
Cycles Containing a Subset of a Given Set of Elements in Cubic Graphs |
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| Sheng BAU.Cycles Containing a Subset of a Given Set of Elements in Cubic Graphs[J].Journal of Mathematical Research with Applications,2013,33(5):543-550. |
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| Authors: | Sheng BAU |
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| Institution: | School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa; Institute of Discrete Mathematics, Inner Mongolia University of Nationalities, Inner Mongolia 028005, P. R. China |
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| Abstract: | The technique of contractions and the known results in the study of cycles in $3$-connected cubic graphs are applied to obtain the following result. Let $G$ be a $3$-connected cubic graph, $X\subseteq V(G)$ with $|X| = 16$ and $e\in E(G)$. Then either for every $8$-subset $A$ of $X$, $A\cup\{e\}$ is cyclable or for some $14$-subset $A$ of $X$, $A\cup\{e\}$ is cyclable. |
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| Keywords: | contraction cubic graphs cyclability |
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