{"title":"Computing the Number and Average Size of Connected Sets in Planar 3-Trees","authors":"Zuwen Luo, Kexiang Xu","doi":"10.1007/s00373-024-02783-8","DOIUrl":null,"url":null,"abstract":"<p>A vertex set in a graph is a connected set if it induces a connected subgraph. For a tree <i>T</i>, each subgraph induced by a connected set of <i>T</i> is actually a subtree of <i>T</i>. The number and average size of subtrees of a tree <i>T</i> 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.</p>","PeriodicalId":12811,"journal":{"name":"Graphs and Combinatorics","volume":"30 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Graphs and Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00373-024-02783-8","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍：
Graphs and Combinatorics is an international journal devoted to research concerning all aspects of combinatorial mathematics. In addition to original research papers, the journal also features survey articles from authors invited by the editorial board.
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