最小度至少为7的图中的多叶生成树

中文摘要 AI 辅助

我们给出一个多项式时间算法，该算法在每个最小度至少为7的连通n顶点图中构造一棵至少具有25200/46189 n > 0.5455 n 个叶子的生成树。此前没有针对最小度为7的特定界：该类图的最佳可用界为11/21 n ≈ 0.5238 n，该界继承自Simarova关于最小度为6的定理。该算法及其分析针对任意最小度δ进行，并产生一个递归，该递归为每个δ给出叶数的显式下界。所得结果改进了所有已知的δ≥7的界；对于δ=8,9,10，这些界分别为0.5850 n、0.6151 n和0.6413 n，并且在论文末尾对δ≤25进行了列表。

英文摘要

We give a polynomial-time algorithm that constructs, in every connected $n$-vertex graph of minimum degree at least $7$, a spanning tree with at least $\frac{25200}{46189}n>0.5455\,n$ leaves. No bound specific to minimum degree $7$ was known: the best bound available for this class was $\frac{11}{21}n\approx0.5238\,n$, inherited from Simarova's theorem for minimum degree~$6$. The algorithm and its analysis are carried out for an arbitrary minimum degree $δ$, and yield a recursion that gives an explicit lower bound on the number of leaves for every $δ$. The resulting bounds improve all previously known ones for every $δ\ge7$; for $δ=8,9,10$ they are $0.5850\,n$, $0.6151\,n$ and $0.6413\,n$, and they are tabulated for $δ\le25$ at the end of the paper.

发表机构

• San José State University（圣何塞州立大学）

机构由 AI 辅助整理，请以论文原文为准。