English

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