Exact Results for Generalized Extremal Problems Forbidding an Even Cycle

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2025-01-08 DOI:10.1002/jgt.23219

Ervin Győri, Zhen He, Zequn Lv, Nika Salia, Casey Tompkins, Kitti Varga, Xiutao Zhu

{"title":"Exact Results for Generalized Extremal Problems Forbidding an Even Cycle","authors":"Ervin Győri, Zhen He, Zequn Lv, Nika Salia, Casey Tompkins, Kitti Varga, Xiutao Zhu","doi":"10.1002/jgt.23219","DOIUrl":null,"url":null,"abstract":"<div>\n \n We determine the maximum number of copies of <math>\n \n <mrow>\n <msub>\n <mi>K</mi>\n \n <mrow>\n <mi>s</mi>\n \n <mo>,</mo>\n \n <mi>s</mi>\n </mrow>\n </msub>\n </mrow></math> in a <math>\n \n <mrow>\n <msub>\n <mi>C</mi>\n \n <mrow>\n <mn>2</mn>\n \n <mi>s</mi>\n \n <mo>+</mo>\n \n <mn>2</mn>\n </mrow>\n </msub>\n </mrow></math>-free <math>\n \n <mrow>\n <mi>n</mi>\n </mrow></math>-vertex graph for all integers <math>\n \n <mrow>\n <mi>s</mi>\n \n <mo>≥</mo>\n \n <mn>2</mn>\n </mrow></math> and sufficiently large <math>\n \n <mrow>\n <mi>n</mi>\n </mrow></math>. Moreover, for <math>\n \n <mrow>\n <mi>s</mi>\n \n <mo>∈</mo>\n \n <mrow>\n <mo>{</mo>\n \n <mrow>\n <mn>2</mn>\n \n <mo>,</mo>\n \n <mn>3</mn>\n </mrow>\n \n <mo>}</mo>\n </mrow>\n </mrow></math> and any integer <math>\n \n <mrow>\n <mi>n</mi>\n </mrow></math>, we obtain the maximum number of cycles of length <math>\n \n <mrow>\n <mn>2</mn>\n \n <mi>s</mi>\n </mrow></math> in an <math>\n \n <mrow>\n <mi>n</mi>\n </mrow></math>-vertex <math>\n \n <mrow>\n <msub>\n <mi>C</mi>\n \n <mrow>\n <mn>2</mn>\n \n <mi>s</mi>\n \n <mo>+</mo>\n \n <mn>2</mn>\n </mrow>\n </msub>\n </mrow></math>-free bipartite graph.\n </div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"109 2","pages":"218-225"},"PeriodicalIF":0.9000,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Graph Theory","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/jgt.23219","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

Abstract

We determine the maximum number of copies of $K_{s, s}$ in a $C_{2 s + 2}$ -free $n$ -vertex graph for all integers $s \geq 2$ and sufficiently large $n$ . Moreover, for $s \in {2, 3}$ and any integer $n$ , we obtain the maximum number of cycles of length $2 s$ in an $n$ -vertex $C_{2 s + 2}$ -free bipartite graph.

查看原文本刊更多论文

禁止偶环的广义极值问题的精确结果

我们确定K的最大拷贝数，对于所有整数，在一个c2s + 2自由的n顶点图中S≥2且n足够大。并且，对于s∈{2,3}和任意整数n，我们得到了n顶点c2s + 2自由中长度为2s的最大循环数由两部分构成的图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .