{"title":"On the oriented diameter of near planar triangulations","authors":"Yiwei Ge , Xiaonan Liu , Zhiyu Wang","doi":"10.1016/j.disc.2025.114406","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we show that the oriented diameter of any <em>n</em>-vertex 2-connected near triangulation is at most <span><math><mo>⌈</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌉</mo></math></span> (except for seven small exceptions), and the upper bound is tight. This extends a result of Wang et al. (2021) <span><span>[29]</span></span> on the oriented diameter of maximal outerplanar graphs, and improves an upper bound of <span><math><mi>n</mi><mo>/</mo><mn>2</mn><mo>+</mo><mi>O</mi><mo>(</mo><msqrt><mrow><mi>n</mi></mrow></msqrt><mo>)</mo></math></span> on the oriented diameter of planar triangulations by Mondal et al. (2024) <span><span>[24]</span></span>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 5","pages":"Article 114406"},"PeriodicalIF":0.7000,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X25000147","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we show that the oriented diameter of any n-vertex 2-connected near triangulation is at most (except for seven small exceptions), and the upper bound is tight. This extends a result of Wang et al. (2021) [29] on the oriented diameter of maximal outerplanar graphs, and improves an upper bound of on the oriented diameter of planar triangulations by Mondal et al. (2024) [24].
期刊介绍：
Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory.
Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.
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