On the complexity of list H-packing for sparse graph classes

IF 1 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS
Tatsuya Gima , Tesshu Hanaka , Yasuaki Kobayashi , Yota Otachi , Tomohito Shirai , Akira Suzuki , Yuma Tamura , Xiao Zhou
{"title":"On the complexity of list H-packing for sparse graph classes","authors":"Tatsuya Gima ,&nbsp;Tesshu Hanaka ,&nbsp;Yasuaki Kobayashi ,&nbsp;Yota Otachi ,&nbsp;Tomohito Shirai ,&nbsp;Akira Suzuki ,&nbsp;Yuma Tamura ,&nbsp;Xiao Zhou","doi":"10.1016/j.tcs.2025.115425","DOIUrl":null,"url":null,"abstract":"<div><div>The problem of packing as many subgraphs isomorphic to some <span><math><mi>H</mi><mo>∈</mo><mi>H</mi></math></span> as possible into a graph, where <span><math><mi>H</mi></math></span> is a collection of graphs, has been well studied in the literature. Both vertex-disjoint and edge-disjoint versions are known to be NP-complete for <em>H</em> that contains at least three vertices and at least three edges, respectively. In this paper, we consider “list variants” of these problems: Given a graph <em>G</em>, an integer <em>k</em>, and a collection <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>H</mi></mrow></msub></math></span> of subgraphs of <em>G</em> isomorphic to some <span><math><mi>H</mi><mo>∈</mo><mi>H</mi></math></span>, the goal is to compute <em>k</em> subgraphs in <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>H</mi></mrow></msub></math></span> that are pairwise vertex- or edge-disjoint. We show several positive and negative results, focusing on classes of sparse graphs, such as bounded-degree graphs, planar graphs, and bounded-treewidth graphs.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1052 ","pages":"Article 115425"},"PeriodicalIF":1.0000,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Computer Science","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304397525003639","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0

Abstract

The problem of packing as many subgraphs isomorphic to some HH as possible into a graph, where H is a collection of graphs, has been well studied in the literature. Both vertex-disjoint and edge-disjoint versions are known to be NP-complete for H that contains at least three vertices and at least three edges, respectively. In this paper, we consider “list variants” of these problems: Given a graph G, an integer k, and a collection LH of subgraphs of G isomorphic to some HH, the goal is to compute k subgraphs in LH that are pairwise vertex- or edge-disjoint. We show several positive and negative results, focusing on classes of sparse graphs, such as bounded-degree graphs, planar graphs, and bounded-treewidth graphs.
稀疏图类列表h填充的复杂度
将尽可能多的同H∈H同构的子图打包到一个图中,其中H是图的集合,这个问题已经在文献中得到了很好的研究。对于分别包含至少三个顶点和至少三条边的H,已知顶点不相交和边不相交的版本都是np完全的。在本文中,我们考虑了这些问题的“列表变体”:给定一个图G,一个整数k,以及G同构于某个H∈H的子图集合LH,目标是计算LH中k个顶点不相交或边不相交的子图。我们给出了几个正负结果,重点讨论了稀疏图的类别,如有界度图、平面图和有界树宽图。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Theoretical Computer Science
Theoretical Computer Science 工程技术-计算机:理论方法
CiteScore
2.60
自引率
18.20%
发文量
471
审稿时长
12.6 months
期刊介绍: Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信