2006/05/07 by Daniela Kühn, Deryk Osthus, Kühn, Daniela +4
Computer Science · Mathematics · #05C20 #05C80 #05C83 #Advanced Graph Theory Research #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph Labeling and Dimension Problems #math.CO #msc:05C20 #msc:05C80 #msc:05C83
paper · pdf · doi:10.48550/arxiv.math/0605178
arxiv created 2006/05/07 · openalex publication_date 2006/05/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Mader conjectured that for all k there is an integer d(k) such that every digraph of minimum outdegree at least d(k) contains a subdivision of a transitive tournament of order k. In this note we observe that if the minimum outdegree of a digraph is sufficiently large compared to its order then one can even guarantee a subdivision of a large complete digraph. More precisely, let G be a digraph of order n whose minimum outdegree is at least d. Then G contains a subdivision of a complete digraph of order at least d2/(8n3/2).