A note on complete subdivisions in digraphs of large outdegree
Combinatorics
2007-05-23 v1
Abstract
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 d^2/(8n^{3/2}).
Keywords
Cite
@article{arxiv.math/0605178,
title = {A note on complete subdivisions in digraphs of large outdegree},
author = {Daniela Kühn and Deryk Osthus and Andrew Young},
journal= {arXiv preprint arXiv:math/0605178},
year = {2007}
}