{"title":"Hypergraph Edge Representations with the Use of Homological Paths","authors":"M. N. Vyalyi, V. E. Karpov","doi":"10.1134/S1990478923030201","DOIUrl":null,"url":null,"abstract":"<p> We consider the problem of realization of hypergraphs on a graph provided each hyperedge\nis realized by a subgraph in which exactly two vertices have odd degree. This problem is related to\nCycle Double Cover conjecture. We prove that checking the existence of realization is\ncomputationally hard. The hardness is proved in various settings: for realizations on all graphs,\non simple graphs, and on graphs from several restricted classes.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 3","pages":"678 - 686"},"PeriodicalIF":0.5800,"publicationDate":"2023-11-04","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/S1990478923030201","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
We consider the problem of realization of hypergraphs on a graph provided each hyperedge
is realized by a subgraph in which exactly two vertices have odd degree. This problem is related to
Cycle Double Cover conjecture. We prove that checking the existence of realization is
computationally hard. The hardness is proved in various settings: for realizations on all graphs,
on simple graphs, and on graphs from several restricted classes.
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
