The maximum number of short paths in a Halin graph

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Discrete Optimization Pub Date : 2023-11-01 DOI:10.1016/j.disopt.2023.100809

Shunhai He , Huiqing Liu

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引用次数: 0

Abstract

A Halin graph $G$ is a plane graph consisting of a plane embedding of a tree $T$ of order at least 4 containing no vertex of degree 2, and of a cycle $C$ connecting all leaves of $T$ . Let $f_{h} (n, G)$ be the maximum number of copies of $G$ in a Halin graph on $n$ vertices. In this paper, we give exact values of $f_{h} (n, G)$ when $G$ is a path on $k$ vertices for $2 \leq k \leq 5$ . Moreover, we develop a new graph transformation preserving the number of vertices, so that the resulting graph has a monotone behavior with respect to the number of short paths.

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Halin图中最短路径的最大数目

Halin图G是一个平面图，由至少为4阶的树T的平面嵌入和连接T的所有叶的循环C的平面嵌入组成。设fh(n,G)为Halin图中n个顶点上G的最大副本数。本文给出了当G是k个顶点上的路径且2≤k≤5时，fh(n,G)的精确值。此外，我们提出了一种保留顶点数的图变换，使得生成的图对短路径数具有单调性。

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 Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.