Refinements of degree conditions for the existence of a spanning tree without small degree stems

IF 0.7 3区数学 Q2 MATHEMATICS Discrete Mathematics Pub Date : 2024-11-05 DOI:10.1016/j.disc.2024.114307

Michitaka Furuya , Akira Saito , Shoichi Tsuchiya

引用次数: 0

Abstract

A spanning tree of a graph without vertices of degree 2 is called a homeomorphically irreducible spanning tree (or a HIST) of the graph. Albertson et al. (1990) [1] gave a minimum degree condition for the existence of a HIST, and recently, Ito and Tsuchiya (2022) [11] found a sharp degree-sum condition for the existence of a HIST. In this paper, we refine these results, and extend the first one to a spanning tree in which no vertex other than the endvertices has small degree.

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细化无小度干生成树存在的度数条件

没有阶数为 2 的顶点的图的生成树称为图的同构不可还原生成树（或 HIST）。Albertson 等人（1990）[1] 给出了 HIST 存在的最小度条件，最近，Ito 和 Tsuchiya（2022）[11] 发现了 HIST 存在的尖锐度和条件。在本文中，我们完善了这些结果，并将第一个结果扩展到了除端顶点外没有其他顶点具有小度的生成树。

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.