Structural parameters of Schnyder woods

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-10-09 DOI:10.1016/j.disc.2024.114282

Christian Ortlieb , Jens M. Schmidt

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.

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施奈德木材的结构参数

我们利用结构相关的方法研究了施奈德林的两个基本参数。首先，我们证明了施奈德林三棵树中叶子总数的新下限。其次，众所周知，施奈德林可以用来寻找三个兼容的有序路径分区。我们证明了这种兼容有序路径分区中单子（即只包含一个顶点的路径）数量的新下界。我们提出的所有界限都很严密。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

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.