Domination parameters and added matchings

IF 0.7 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2025-07-23 DOI:10.1007/s00010-025-01196-z

Wayne Goddard, Michael A. Henning

引用次数: 0

Abstract

We consider the augmentation problem of how domination parameters behave when a perfect matching P of the complement is added to the graph. We focus on the case that the graph is a tree, and inter alia show that if T is a tree of even order n that is not a star, then \(T+P\) has domination number at most 2n/5, independent domination number at most \(n/2-1\), and total domination and upper domination number at most n/2. Further, there exists a choice of P such that \(T+P\) has total domination number at most n/3. All these bounds are sharp.

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控制参数和添加的匹配

我们考虑了在图中加入补的完全匹配P时控制参数的增广问题。我们主要讨论了图是树的情况，并特别证明了如果T是一棵非星形的偶数阶n树，那么\(T+P\)的统治数最多为2n/5，独立统治数最多为\(n/2-1\)，总统治数和上统治数最多为n/2。进一步，存在一个P的选择，使得\(T+P\)的总统治数最多为n/3。所有这些界限都很明显。

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

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.