On the cycle isolation number of triangle-free graphs

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-08-01 DOI:10.1016/j.disc.2024.114190

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引用次数: 0

Abstract

For a graph G, a subset $S \subseteq V (G)$ is called a cycle isolating set of G if $G - N [D]$ contains no cycle. The cycle isolation number of G, denoted by $ι_{c} (G)$ , is the minimum cardinality of a cycle isolating set of G. Recently, Borg proved that if G is a connected n-vertex graph that is not a triangle, then $ι_{c} (G) \leq \frac{n}{4}$ . In this paper, we prove that if G is a connected triangle-free n-vertex graph that is not a 4-cycle, then $ι_{c} (G) \leq \frac{n}{5}$ . In particular, we characterize the subcubic graphs that attain the bound. For graphs with larger girth, several conjectures are proposed.

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关于无三角形图形的循环隔离数

对于图 G，如果 G-N[D] 不包含循环，则子集 S⊆V(G)称为 G 的循环隔离集。最近，博格（Borg）证明了如果 G 是一个非三角形的 n 顶点连通图，则 ιc(G)≤n4。在本文中，我们证明了如果 G 是一个非 4 循环的无三角形 n 顶点连通图，则 ιc(G)≤n5。我们特别描述了达到该界限的亚立方图的特征。对于周长较大的图，我们提出了几个猜想。

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.