On topological tournaments of order 4 in digraphs of outdegree 3
Journal of Graph Theory
A note on complete subdivisions in digraphs of large outdegree
Journal of Graph Theory
Graph Theory
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
| Hi-index | 0.00 |
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 the minimum degree is at least t(t-1), and, for t@?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 indegree and outdegree which do not contain an immersion of the complete digraph on three 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.