A note on complete subdivisions in digraphs of large outdegree

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Mader conjectured that for all l there is an integer delta(+)(l) such that every digraph of minimum outdegree at least delta(+)(l) contains a subdivision of a transitive tournament of order l. 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) over bar be a digraph of order n whose minimum outdegree is at least d. Then (G) over bar contains a subdivision of a complete digraph of order left perpendicular d(2)/(8n(3/2)) right perpendicular. (c) 2007 Wiley Periodicals, Inc.
Original languageEnglish
Pages (from-to)1-6
Number of pages6
JournalJournal of Graph Theory
Issue number1
Early online date1 Jan 2007
Publication statusPublished - 1 Jan 2008


  • subdivision
  • digraph
  • topological minor


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