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Pré-Publication, Document De Travail Année : 2024

The 3-dicritical semi-complete digraphs

Résumé

A digraph is $3$-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 $3$-dicritical digraph.
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hal-04471658 , version 1 (21-02-2024)

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Frédéric Havet, Florian Hörsch, Lucas Picasarri-Arrieta. The 3-dicritical semi-complete digraphs. 2024. ⟨hal-04471658⟩
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