Dipaths of length at least double the minimum outdegree
Combinatorics
2023-03-21 v3
Abstract
A special case of a conjecture by Thomass\'e is that any oriented graph with minimum outdegree k contains a dipath of length 2k. For the sake of proving whether or not a counterexample exists, we present reductions and establish bounds on both connectivity and the number of vertices in a counterexample. We further conjecture that in any oriented graph with minimum outdegree k, every vertex belongs to a dipath of length 2k.
Keywords
Cite
@article{arxiv.1608.03259,
title = {Dipaths of length at least double the minimum outdegree},
author = {Joe DeLong},
journal= {arXiv preprint arXiv:1608.03259},
year = {2023}
}
Comments
This research is too basic, and I don't wish to waste anyone's time on it