 Cycles Containing a Subset of a Given Set of Elements in Cubic Graphs
Cycles Containing a Subset of a Given Set of Elements in Cubic Graphs

DOI：10.3770/j.issn:2095-2651.2013.05.003

 作者 单位 宝升 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

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.

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.