Forcing, anti-forcing, global forcing and complete forcing on perfect matchings of graphs — A survey

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-07-03 DOI:10.1016/j.dam.2025.06.022

Yaxian Zhang , Xin He , Qianqian Liu , Heping Zhang

引用次数: 0

Abstract

The notion of forcing number for a perfect matching or innate degree of freedom for a Kekulé structure was introduced by Randić and Klein in 1980s, which plays an important role in the resonance theory in organic chemistry. Over the past four decades, some theoretical chemists and mathematicians have been attracted to investigate the effects in some chemical graphs and the graph-theoretical problems in general graphs. Recently some derived concepts and related problems have also been raised successively, such as anti-forcing number of a perfect matching, global forcing number, complete forcing number, etc. This survey will present recent progress on the minimum and maximum (anti-) forcing numbers, (anti-) forcing spectra and (anti-) forcing polynomials of perfect matchings of graphs, and global forcing and complete forcing numbers with their relations, as well as some open problems and conjectures.

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图的完美匹配的强迫、反强迫、整体强迫和完全强迫——综述

kekul结构完全匹配或固有自由度的强迫数概念是randiki和Klein在20世纪80年代提出的，在有机化学共振理论中起着重要作用。在过去的四十年里，一些理论化学家和数学家被吸引来研究一些化学图中的效应和一般图中的图论问题。近年来也相继提出了一些衍生的概念和相关问题，如完全匹配的反强迫数、全局强迫数、完全强迫数等。本文将介绍图的完全匹配的最小和最大（反）强迫数、（反）强迫谱和（反）强迫多项式、全局强迫数和完全强迫数及其关系的最新进展，以及一些开放的问题和猜想。

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 Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.