Immersing complete digraphs
Combinatorics
2011-09-20 v1
Abstract
We consider the problem of immersing the complete digraph on t vertices in a simple digraph. For Eulerian digraphs, we show that such an immersion always exists whenever minimum degree is at least t(t-1), and for t at most 4 minimum degree at least t-1 suffices. On the other hand, we show that there exist non-Eulerian digraphs with all vertices of arbitrarily high in- and outdegree which do not contain an immersion of the complete digraph on 3 vertices. As a side result, we obtain a construction of digraphs with large outdegree in which all cycles have odd length, simplifying a former construction of such graphs by Thomassen.
Keywords
Cite
@article{arxiv.1109.3741,
title = {Immersing complete digraphs},
author = {Matt DeVos and Jessica McDonald and Bojan Mohar and Diego Scheide},
journal= {arXiv preprint arXiv:1109.3741},
year = {2011}
}