A note on complete subdivisions in digraphs of large outdegree

Mader conjectured that for all there is an integer + ( ) such that every digraph of minimum outdegree at least + ( ) contains a subdivision of a transitive tournament of order . 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 d2 /(8n3/2 ) .

• Type: Journal
• Year: 2008
• Where: JGT
• Authors: Daniela Kühn, Deryk Osthus, Andrew Young
• Keywords: JGT 2008, Mader, Minimum Outdegree, Transitive Tournament