Forest cuts in sparse graphs

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-05-27 DOI:10.1016/j.disc.2025.114594

Vsevolod Chernyshev , Johannes Rauch , Dieter Rautenbach

引用次数: 0

Abstract

We consider the conjecture that every graph G of order n with less than

3 n - 6

edges has a vertex cut that induces a forest. Maximal planar graphs do not have such vertex cuts and show that the density condition would be best possible. We verify the conjecture for planar graphs and show that every graph G of order n with less than

\frac{11}{5} n - \frac{18}{5}

edges has a vertex cut that induces a forest.

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稀疏图中的森林砍伐

我们考虑这样一个猜想：每一个边数小于3n−6的n阶图G都有一个顶点切割，该顶点切割可以诱导出一个森林。最大的平面图没有这样的顶点切割，并表明密度条件将是最好的。我们验证了平面图的猜想，并证明了每一个小于115n−185条边的n阶图G都有一个顶点切割，可以诱导出一个森林。

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.