{"title":"Faster algorithms and a smaller kernel for Cliques or Trees Vertex Deletion","authors":"Dekel Tsur","doi":"10.1016/j.ipl.2025.106570","DOIUrl":null,"url":null,"abstract":"<div><div>In the <span>Cliques or Trees Vertex Deletion</span> problem, the input is a graph <em>G</em> and an integer <em>k</em>, and the goal is to decide whether there is a set of at most <em>k</em> vertices whose removal from <em>G</em> result in a graph in which every connected component is either a clique or a tree. In this paper we give an <span><math><msup><mrow><mi>O</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><msup><mrow><mn>3.46</mn></mrow><mrow><mi>k</mi></mrow></msup><mo>)</mo></math></span>-time deterministic algorithm, an <span><math><msup><mrow><mi>O</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><msup><mrow><mn>3.103</mn></mrow><mrow><mi>k</mi></mrow></msup><mo>)</mo></math></span>-time randomized algorithm, and a kernel with <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>)</mo></math></span> vertices for <span>Cliques or Trees Vertex Deletion</span>.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106570"},"PeriodicalIF":0.7000,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Information Processing Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020019025000146","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
In the Cliques or Trees Vertex Deletion problem, the input is a graph G and an integer k, and the goal is to decide whether there is a set of at most k vertices whose removal from G result in a graph in which every connected component is either a clique or a tree. In this paper we give an -time deterministic algorithm, an -time randomized algorithm, and a kernel with vertices for Cliques or Trees Vertex Deletion.
期刊介绍：
Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered.
Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.
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