论文标题
根据图表的叶子数估计图的圆周
Estimating the circumference of a graph in terms of its leaf number
论文作者
论文摘要
令$ \ mathcal {t} $为$ g $的一组生成树，让$ l（t）$为树$ t $中的叶子数。 $ g $的叶数$ l（g）$定义为$ l（g）= \ max \ {l（t）| t \ in \ Mathcal {t} \} $。令$ g $为订单$ n $和最低度$δ$的连接图，以便$ l（g）\ leq2δ-1$。我们表明，$ g $的周长至少是$ n-1 $，如果$ g $是常规的，那么$ g $是汉密尔顿人。
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.
