根据图形的叶片数估算图形的周长

Jingru Yan
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引用次数: 0

摘要

让 \(\mathcal {T}\)是图 G 的生成树集合,让 L(T) 是树 T 中叶子的数量。让 G 是一个阶数为 n 且最小度数为 \(\delta \)的连通图,使得 \(L(G)\le 2\delta -1\).我们证明 G 的周长至少是 \(n-1\),如果 G 是正则图,那么 G 就是哈密顿图。
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Estimating the circumference of a graph in terms of its leaf number

Let \(\mathcal {T}\) be the set of spanning trees of a graph 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 \(\delta \) such that \(L(G)\le 2\delta -1\). 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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