随机图中二部图的饱和数

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-05-05 DOI:10.1016/j.disc.2025.114561

Meysam Miralaei , Ali Mohammadian , Behruz Tayfeh-Rezaie , Maksim Zhukovskii

{"title":"随机图中二部图的饱和数","authors":"Meysam Miralaei , Ali Mohammadian , Behruz Tayfeh-Rezaie , Maksim Zhukovskii","doi":"10.1016/j.disc.2025.114561","DOIUrl":null,"url":null,"abstract":"<div><div>For a given graph F, the F-saturation number of a graph G, denoted by <math><mrow><mi>sat</mi></mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>F</mi><mo>)</mo></math>, is the minimum number of edges in an edge-maximal F-free subgraph of G. In 2017, Korándi and Sudakov determined <figure><img></figure> asymptotically, where <figure><img></figure> denotes the Erdős–Rényi random graph and <math><msub><mrow><mi>K</mi></mrow><mrow><mi>r</mi></mrow></msub></math> is the complete graph on r vertices. In this paper, among other results, we present an asymptotic upper bound on <figure><img></figure> for any bipartite graph F and also an asymptotic lower bound on <figure><img></figure> for any complete bipartite graph F.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 9","pages":"Article 114561"},"PeriodicalIF":0.7000,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Saturation numbers of bipartite graphs in random graphs\",\"authors\":\"Meysam Miralaei , Ali Mohammadian , Behruz Tayfeh-Rezaie , Maksim Zhukovskii\",\"doi\":\"10.1016/j.disc.2025.114561\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>For a given graph F, the F-saturation number of a graph G, denoted by <math><mrow><mi>sat</mi></mrow><mo>(</mo><mi>G</mi><mo>,</mo><mi>F</mi><mo>)</mo></math>, is the minimum number of edges in an edge-maximal F-free subgraph of G. In 2017, Korándi and Sudakov determined <figure><img></figure> asymptotically, where <figure><img></figure> denotes the Erdős–Rényi random graph and <math><msub><mrow><mi>K</mi></mrow><mrow><mi>r</mi></mrow></msub></math> is the complete graph on r vertices. In this paper, among other results, we present an asymptotic upper bound on <figure><img></figure> for any bipartite graph F and also an asymptotic lower bound on <figure><img></figure> for any complete bipartite graph F.</div></div>\",\"PeriodicalId\":50572,\"journal\":{\"name\":\"Discrete Mathematics\",\"volume\":\"348 9\",\"pages\":\"Article 114561\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-05-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0012365X25001694\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X25001694","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

摘要

对于给定的图F，图G的F饱和数，用sat（G，F）表示，是G的最大边无F子图的最小边数。2017年，Korándi和Sudakov渐近确定，其中表示Erdős-Rényi随机图，Kr是r个顶点上的完全图。本文给出了任意二部图F的渐近上界和任意完全二部图F的渐近下界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Saturation numbers of bipartite graphs in random graphs

For a given graph F, the F-saturation number of a graph G, denoted by

sat (G, F)

, is the minimum number of edges in an edge-maximal F-free subgraph of G. In 2017, Korándi and Sudakov determined

asymptotically, where

denotes the Erdős–Rényi random graph and

K_{r}

is the complete graph on r vertices. In this paper, among other results, we present an asymptotic upper bound on

for any bipartite graph F and also an asymptotic lower bound on

for any complete bipartite graph F.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.