{"title":"Tight Bound on Treedepth in Terms of Pathwidth and Longest Path","authors":"","doi":"10.1007/s00493-023-00077-w","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>We show that every graph with pathwidth strictly less than <em>a</em> that contains no path on <span> <span>\\(2^b\\)</span> </span> vertices as a subgraph has treedepth at most 10<em>ab</em>. The bound is best possible up to a constant factor.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"34 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Combinatorica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00493-023-00077-w","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We show that every graph with pathwidth strictly less than a that contains no path on \(2^b\) vertices as a subgraph has treedepth at most 10ab. The bound is best possible up to a constant factor.
期刊介绍：
COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are
- Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups).
- Combinatorial optimization.
- Combinatorial aspects of geometry and number theory.
- Algorithms in combinatorics and related fields.
- Computational complexity theory.
- Randomization and explicit construction in combinatorics and algorithms.
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