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Various bounds on the minimum number of arcs in a -dicritical digraph
Pierre Aboulker, Quentin Vermande
The dichromatic number of a digraph is the least integer such that can be partitioned into acyclic digraphs. A digraph is -dicritical if $\vecχ(G) = k…
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…
Heroes in orientations of chordal graphs
Pierre Aboulker, Guillaume Aubian, Raphael Steiner
We characterize all digraphs such that orientations of chordal graphs with no induced copy of have bounded dichromatic number.
Vizing's and Shannon's Theorems for defective edge colouring
Pierre Aboulker, Guillaume Aubian, Chien-Chung Huang
We call a multigraph -edge colourable if its edge set can be partitioned into subgraphs of maximum degree at most and denote as the minimum such that…
Chordal directed graphs are not -bounded
Pierre Aboulker, Nicolas Bousquet, Rémi de Verclos
We show that digraphs with no transitive tournament on vertices and in which every induced directed cycle has length can have arbitrarily large dichromatic number. This ans…
Heroes in oriented complete multipartite graphs
Pierre Aboulker, Guillaume Aubian, Pierre Charbit
The dichromatic number of a digraph is the minimum size of a partition of its vertices into acyclic induced subgraphs. Given a class of digraphs , a digraph is a he…