From the 1 of 16 linked papers with an AI index.
16 papers
Acyclic Dichromatic Number of Tournaments: these are the Champions
Pierre Aboulker, Pierre Charbit, Samuel Coulomb +2
The paper characterizes the subtournaments that must occur in any tournament with a sufficiently large acyclic dichromatic number, confirming a conjecture and establishing a local‑…
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…
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…
Edge-colouring and orientations: applications to degree- and -boundedness
Arnab Char, Ken-ichi Kawarabayashi, Lucas Picasarri-Arrieta
We prove a new generalisation of Ramsey's theorem by showing that every -edge-coloured graph with sufficiently large minimum degree contains a monochromatic induced subgraph who…
On the list version of a conjecture of ErdÅs 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 acy…
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-Î…