The 3-Dicritical Semi-Complete Digraphs

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 collection of 3-dicritical semi-complete digraphs is finite. Further, we give a computer-assisted proof of a full ch...

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Bibliographic Details
Published inThe Electronic journal of combinatorics Vol. 32; no. 1
Main Authors Havet, Frédéric, Hörsch, Florian, Picasarri-Arrieta, Lucas
Format Journal Article
LanguageEnglish
Published 17.01.2025
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Summary: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 collection 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.
ISSN:1077-8926
1077-8926
DOI:10.37236/12820