2 citations · 2 across the 4 of their papers we have counts for
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Minimum acyclic number and maximum dichromatic number of oriented triangle-free graphs of a given order
Pierre Aboulker, Frédéric Havet, François Pirot +1
Let be a digraph. Its acyclic number is the maximum order of an acyclic induced subdigraph and its dichromatic number is the least integer such that $…
The 3-dicritical semi-complete digraphs
Frédéric Havet, Florian Hörsch, Lucas Picasarri-Arrieta
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…
On the minimum number of arcs in -dicritical oriented graphs
Pierre Aboulker, Thomas Bellitto, Frédéric Havet +1
The dichromatic number $\dic(D)$ of a digraph is the least integer such that can be partitioned into directed acyclic digraphs. A digraph is -dicritical if $\dic…
Subdivisions in digraphs of large out-degree or large dichromatic number
Pierre Aboulker, Nathann Cohen, Fréderic Havet +3
In 1985, Mader conjectured the existence of a function such that every digraph with minimum out-degree at least contains a subdivision of the transitive tournament of or…