On a property of 2-connected graphs and Dirac's Theorem

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-07-14 DOI:10.1016/j.disc.2024.114153

Alexandr Kostochka , Ruth Luo , Grace McCourt

引用次数: 0

Abstract

We refine a property of 2-connected graphs described in the classical paper of Dirac from 1952 and use the refined property to somewhat shorten Dirac's proof of the fact that each 2-connected n-vertex graph with minimum degree at least k has a cycle of length at least $\min {n, 2 k}$ .

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关于 2 连接图的一个属性和狄拉克定理

我们完善了 1952 年狄拉克经典论文中描述的 2 连接图的一个性质，并利用这一完善的性质在一定程度上缩短了狄拉克对以下事实的证明：每个最小度至少为 k 的 2 连接 n 顶点图至少有一个长度为 min{n,2k} 的循环。

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.