{"title":"Immersion of complete digraphs in Eulerian digraphs","authors":"António Girão, Shoham Letzter","doi":"10.1007/s11856-023-2572-y","DOIUrl":null,"url":null,"abstract":"Abstract A digraph G immerses a digraph H if there is an injection f : V ( H ) → V ( G ) and a collection of pairwise edge-disjoint directed paths P uv , for uv ∈ E ( H ), such that P uv starts at f ( u ) and ends at f ( v ). We prove that every Eulerian digraph with minimum out-degree t immerses a complete digraph on Ω( t ) vertices, thus answering a question of DeVos, McDonald, Mohar and Scheide.","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Israel Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11856-023-2572-y","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
Abstract A digraph G immerses a digraph H if there is an injection f : V ( H ) → V ( G ) and a collection of pairwise edge-disjoint directed paths P uv , for uv ∈ E ( H ), such that P uv starts at f ( u ) and ends at f ( v ). We prove that every Eulerian digraph with minimum out-degree t immerses a complete digraph on Ω( t ) vertices, thus answering a question of DeVos, McDonald, Mohar and Scheide.
期刊介绍：
The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.
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