The 3-dicritical semi-complete digraphs
Combinatorics
2024-02-22 v2
Abstract
A digraph is -dicritical if it cannot be vertex-partitioned into two sets inducing acyclic digraphs, but each of its proper subdigraphs can. We give a human-readable proof that the number of 3-dicritical semi-complete digraphs is finite. Further, we give a computer-assisted proof of a full characterization of 3-dicritical semi-complete digraphs. There are eight such digraphs, two of which are tournaments. We finally give a general upper bound on the maximum number of arcs in a -dicritical digraph.
Keywords
Cite
@article{arxiv.2402.12014,
title = {The 3-dicritical semi-complete digraphs},
author = {Frédéric Havet and Florian Hörsch and Lucas Picasarri-Arrieta},
journal= {arXiv preprint arXiv:2402.12014},
year = {2024}
}