24 papers
Acyclic Dichromatic Number of Tournaments: these are the Champions
Pierre Aboulker, Pierre Charbit, Samuel Coulomb +2
The acyclic dichromatic number of an oriented graph is the minimum size of a vertex-partition such that the digraphs induced by any single part are acyclic, and the oriented bipart…
Coloring digraphs with colors
Ken-ichi Kawarabayashi, Lucas Picasarri-Arrieta
The dichromatic number of a digraph is the minimum number of colors needed to partition its vertex set into acyclic subdigraphs. A biclique is a set of vertices inducing all possib…
On the list version of a conjecture of Erdős and Neumann-Lara
Ararat Harutyunyan, Lucas Picasarri-Arrieta, Gil Puig i Surroca
The dichromatic number of a digraph , denoted by , is the smallest number of colours required to colour the vertices of such that each colour class induces an acyc…
Increasing arc-connectivity by bounded- and fixed-size inversions
Florian Hörsch, Lucas Picasarri-Arrieta
For a digraph and some , the inversion of is the operation of flipping all arcs both of whose endvertices are in . We initiate the study of establishin…
On the number of maximal independent sets and maximal induced bipartite subgraphs in -free graphs
Thilo Hartel, Lucas Picasarri-Arrieta, Dieter Rautenbach
Let be a -free graph of order and let be an integer with . We show the existence of positive constants and such that has at most $(4-η)^…
Acyclic dichromatic number of oriented graphs
Jørgen Bang-Jensen, Lucas Picasarri-Arrieta, Anders Yeo
The dichromatic number of a digraph is the minimum number of sets in a partition of into subsets so that the induced subdigraph $D[V…