用图的叶数估计图的周长
Estimating the circumference of a graph in terms of its leaf number
摘要：
令$\mathcal{T}$是$G$的生成树的集合，并且令$L(T)$是树$T$中的叶子的数目。$G$的叶编号$L(G)$定义为$L(G)=\max\{L(T)|T\in \mathcal{T}\}$。设$G$是阶$n$和最小度$δ$的连通图，使得$L(G)\leq 2δ-1$ .我们证明了$G$的周长至少为$n-1$，并且如果$G$是正则的，则$G$是Hamilton的.
英文摘要：
Let $\mathcal{T}$ be the set of spanning trees of $G$ and let $L(T)$ be the number of leaves in a tree $T$. The leaf number $L(G)$ of $G$ is defined as $L(G)=\max\{L(T)|T\in \mathcal{T}\}$. Let $G$ be a connected graph of order $n$ and minimum degree $δ$ such that $L(G)\leq 2δ-1$. We show that the circumference of $G$ is at least $n-1$, and that if $G$ is regular then $G$ is hamiltonian.
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