六边形图的三路径顶点覆盖和解离数

IF 1 4区数学 Q1 MATHEMATICS

Applicable Analysis and Discrete Mathematics Pub Date : 2022-01-01 DOI:10.2298/aadm201009007e

Rija Erveš, Aleksandra Tepeh

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引用次数: 1

摘要

如果图G中k阶的每条路径至少包含一个来自P的顶点，则图G的顶点子集P称为k路径顶点覆盖。最小k路径顶点覆盖的基数称为G的k路径顶点覆盖数，用?k(G)表示。众所周知，寻找最小3路径顶点覆盖的问题对于平面图来说是np困难的。本文建立了?3(G)的上界，其中G来自一个重要的平面图族，称为六边形图，是在实际应用中产生的。

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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3-path vertex cover and dissociation number of hexagonal graphs

A subset P of vertices of a graph G is called a k-path vertex cover if every path of order k in G contains at least one vertex from P. The cardinality of a minimum k-path vertex cover is called the k-path vertex cover number of G, and is denoted by ?k(G). It is known that the problem of finding a minimum 3-path vertex cover is NP-hard for planar graphs. In this paper we establish an upper bound for ?3(G), where G is from an important family of planar graphs, called hexagonal graphs, arising from real world applications.

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来源期刊

Applicable Analysis and Discrete Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).