The maximum number of cliques in graphs with given fractional matching number and minimum degree

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-09-16 DOI:10.1016/j.dam.2025.09.010

Chengli Li, Yurui Tang

引用次数: 0

Abstract

Recently, Ma, Qian and Shi determined the maximum size of an

n

-vertex graph with given fractional matching number

s

and maximum degree at most

d

. Motivated by this result, we determine the maximum number of

ℓ

-cliques in a graph with given fractional matching number and minimum degree, which generalizes Shi and Ma’s result about the maximum size of a graph with given fractional matching number and minimum degree at least one. We also determine the maximum number of complete bipartite graphs in a graph with prescribed fractional matching number and minimum degree.

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给定分数匹配数和最小度的图中团的最大数目

最近，Ma、Qian和Shi确定了给定分数匹配数为s且最大度不超过d的n顶点图的最大大小。在此结果的推动下，我们确定了给定分数匹配数和最小度的n顶点图的最大数量，推广了Shi和Ma关于给定分数匹配数和最小度至少为1的图的最大大小的结果。我们还确定了给定分数匹配数和最小度的图中完全二部图的最大数目。

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.