计算平面 3 树中连接集的数量和平均大小

Pub Date : 2024-04-17 DOI:10.1007/s00373-024-02783-8

Zuwen Luo, Kexiang Xu

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引用次数: 0

摘要

如果图中的一个顶点集能诱导出一个连通的子图，那么这个顶点集就是一个连通集。对于树 T 而言，T 的连通集所诱导的每个子图实际上都是 T 的一棵子树。Yan 和 Yeh 提出了一种通过 "生成函数 "计算树中子树数量的线性时间算法。本文提出了计算平面 3 树中连通集的数量和平均大小的线性时间算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Computing the Number and Average Size of Connected Sets in Planar 3-Trees

A vertex set in a graph is a connected set if it induces a connected subgraph. For a tree T, each subgraph induced by a connected set of T is actually a subtree of T. The number and average size of subtrees of a tree T are two well-studied parameters. Yan and Yeh developed a linear-time algorithm for computing the number of subtrees in a tree through “generating function”. In this paper, we present linear-time algorithms for computing the number and average size of connected sets in a planar 3-tree.

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