{"title":"The outerplanar Turán number of disjoint copies of paths","authors":"Jin Li , Yongxin Lan , Changqing Xu","doi":"10.1016/j.amc.2025.129296","DOIUrl":null,"url":null,"abstract":"<div><div>A graph without a copy of <em>T</em> as a subgraph is called <em>T</em>-free. The outerplanar Turán number <span><math><mi>e</mi><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow></mrow><mrow><mi>O</mi><mi>P</mi></mrow></msub></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mi>T</mi><mo>)</mo></math></span> of <em>T</em> represents the maximum number of edges among all <em>n</em>-vertex <em>T</em>-free outerplanar graphs. In this paper, we investigate <span><math><mi>e</mi><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow></mrow><mrow><mi>O</mi><mi>P</mi></mrow></msub></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mi>r</mi><msub><mrow><mi>P</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>)</mo></math></span> and determine its exact value for <span><math><mi>r</mi><mo>,</mo><mi>s</mi><mo>≥</mo><mn>2</mn></math></span> and <span><math><mi>n</mi><mo>≥</mo><mi>r</mi><mi>s</mi></math></span>. This extends a result of Fang and Zhai (2023) <span><span>[7]</span></span>.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"494 ","pages":"Article 129296"},"PeriodicalIF":3.5000,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300325000232","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
A graph without a copy of T as a subgraph is called T-free. The outerplanar Turán number of T represents the maximum number of edges among all n-vertex T-free outerplanar graphs. In this paper, we investigate and determine its exact value for and . This extends a result of Fang and Zhai (2023) [7].
期刊介绍：
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.
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