{"title":"On the Maximum Number of Open Triangles in Graphs with\nFew Edges","authors":"A. V. Pyatkin","doi":"10.1134/S1990478924030128","DOIUrl":null,"url":null,"abstract":"<p> A three-vertex subset is called an open triangle (OT) if it induces a subgraph with exactly\ntwo edges. The problem of finding graphs with maximum number of OTs is considered. It is\nproved that, in case of sufficiently many vertices, such a graph is unique in the class of graphs\nwith constant difference between the numbers of edges and vertices.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 3","pages":"516 - 520"},"PeriodicalIF":0.5800,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478924030128","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
A three-vertex subset is called an open triangle (OT) if it induces a subgraph with exactly
two edges. The problem of finding graphs with maximum number of OTs is considered. It is
proved that, in case of sufficiently many vertices, such a graph is unique in the class of graphs
with constant difference between the numbers of edges and vertices.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
