{"title":"Structural parameters of Schnyder woods","authors":"Christian Ortlieb , Jens M. Schmidt","doi":"10.1016/j.disc.2024.114282","DOIUrl":null,"url":null,"abstract":"<div><div>We study two fundamental parameters of Schnyder woods by exploiting structurally related methods. First, we prove a new lower bound on the total number of leaves in the three trees of a Schnyder wood. Second, it is well-known that Schnyder woods can be used to find three compatible ordered path partitions. We prove new lower bounds on the number of singletons, i.e. paths that consists of exactly one vertex, in such compatible ordered path partitions. All bounds that we present are tight.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 2","pages":"Article 114282"},"PeriodicalIF":0.7000,"publicationDate":"2024-10-09","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/S0012365X24004138","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
We study two fundamental parameters of Schnyder woods by exploiting structurally related methods. First, we prove a new lower bound on the total number of leaves in the three trees of a Schnyder wood. Second, it is well-known that Schnyder woods can be used to find three compatible ordered path partitions. We prove new lower bounds on the number of singletons, i.e. paths that consists of exactly one vertex, in such compatible ordered path partitions. All bounds that we present are tight.
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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