{"title":"外平面Turán路径不相交副本的数目","authors":"Jin Li, Yongxin Lan, Changqing Xu","doi":"10.1016/j.amc.2025.129296","DOIUrl":null,"url":null,"abstract":"A graph without a copy of <ce:italic>T</ce:italic> as a subgraph is called <ce:italic>T</ce:italic>-free. The outerplanar Turán number <mml:math altimg=\"si1.svg\"><mml:mi>e</mml:mi><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mrow></mml:mrow><mml:mrow><mml:mi>O</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:math> of <ce:italic>T</ce:italic> represents the maximum number of edges among all <ce:italic>n</ce:italic>-vertex <ce:italic>T</ce:italic>-free outerplanar graphs. In this paper, we investigate <mml:math altimg=\"si2.svg\"><mml:mi>e</mml:mi><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mrow></mml:mrow><mml:mrow><mml:mi>O</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>r</mml:mi><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=\"false\">)</mml:mo></mml:math> and determine its exact value for <mml:math altimg=\"si3.svg\"><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:math> and <mml:math altimg=\"si4.svg\"><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:mi>r</mml:mi><mml:mi>s</mml:mi></mml:math>. This extends a result of Fang and Zhai (2023) <ce:cross-ref ref>[7]</ce:cross-ref>.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"205 1","pages":""},"PeriodicalIF":3.5000,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":\"A graph without a copy of <ce:italic>T</ce:italic> as a subgraph is called <ce:italic>T</ce:italic>-free. The outerplanar Turán number <mml:math altimg=\\\"si1.svg\\\"><mml:mi>e</mml:mi><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mrow></mml:mrow><mml:mrow><mml:mi>O</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub><mml:mo stretchy=\\\"false\\\">(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy=\\\"false\\\">)</mml:mo></mml:math> of <ce:italic>T</ce:italic> represents the maximum number of edges among all <ce:italic>n</ce:italic>-vertex <ce:italic>T</ce:italic>-free outerplanar graphs. In this paper, we investigate <mml:math altimg=\\\"si2.svg\\\"><mml:mi>e</mml:mi><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mrow></mml:mrow><mml:mrow><mml:mi>O</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub><mml:mo stretchy=\\\"false\\\">(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>r</mml:mi><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo stretchy=\\\"false\\\">)</mml:mo></mml:math> and determine its exact value for <mml:math altimg=\\\"si3.svg\\\"><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi><mml:mo>≥</mml:mo><mml:mn>2</mml:mn></mml:math> and <mml:math altimg=\\\"si4.svg\\\"><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:mi>r</mml:mi><mml:mi>s</mml:mi></mml:math>. This extends a result of Fang and Zhai (2023) <ce:cross-ref ref>[7]</ce:cross-ref>.\",\"PeriodicalId\":55496,\"journal\":{\"name\":\"Applied Mathematics and Computation\",\"volume\":\"205 1\",\"pages\":\"\"},\"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://doi.org/10.1016/j.amc.2025.129296\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1016/j.amc.2025.129296","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
不包含T的子图称为无T图。T的外平面Turán number exOP（n，T）表示所有n顶点无T的外平面图的最大边数。本文研究了exOP（n,rPs）在r、s≥2和n≥rs条件下的精确值。这延伸了Fang和Zhai (2023) b[7]的结果。
The outerplanar Turán number of disjoint copies of paths
A graph without a copy of T as a subgraph is called T-free. The outerplanar Turán number exOP(n,T) of T represents the maximum number of edges among all n-vertex T-free outerplanar graphs. In this paper, we investigate exOP(n,rPs) and determine its exact value for r,s≥2 and n≥rs. 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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