Lucas Picasarri-Arrieta

Bio

As of August 2024, I am a postdoctoral researcher at the National Institute of Informatics (NII) in Tokyo working with Ken-ichi Kawarabayashi. I obtained my PhD (manuscript, slides) in June 2024 at Université Côte D'Azur (Nice), under the supervision of Frédéric Havet and Stéphane Bessy.
My main interests lie in combinatorics and theoretical computer science. In particular, I am interested in graph colouring, directed graphs, reconfiguration, extremal combinatorics and probabilistic methods applied to these areas.

Chromatic discrepancy of locally 𝑠-colourable graphs
with T. Corsini, T. Pierron, F. Pirot, and E. Robinson, 2025.
(𝚫−1)-dicolouring of digraphs
with A. Harutyunyan, K. Kawarabayashi, and G. Puig i Surroca, 2025.
Edge-colouring and orientations: applications to degree-boundedness and 𝛘-boundedness
with A. Char and K. Kawarabayashi, 2025.
Backbone colouring of chordal graphs
with J. Araújo and N. Nisse, 2025.
Blow-ups and extensions of trees in tournaments
with P. Aboulker, F. Havet, W. Lochet, R. Lopes, and C. Rambaud, 2024.
Brooks-type colourings of digraphs in linear time
with D. Gonçalves and A. Reinald, 2024.

Dichromatic number of chordal graphs
with S. Bessy and F. Havet, in Graphs and Combinatorics.
An analogue of Reed's conjecture for digraphs
with K. Kawarabayashi, in the proceedings of SODA 2025.
The 3-dicritical semi-complete digraphs
with F. Havet and F. Hörsch, in The Electronic Journal of Combinatorics.

Complexity results on the decomposition of a digraph into directed linear forests and out-stars
with F. Hörsch, in The Electronic Journal of Combinatorics.
On the minimum number of arcs in 4-dicritical oriented graphs
with F. Havet and C. Rambaud, in Journal of Graph Theory.
Short version in the proceedings of WG'23.
Subdivisions in dicritical digraphs with large order or digirth
with C. Rambaud, in European Journal of Combinatorics.
Constrained Flows in Networks
with S. Bessy and J. Bang-Jensen, in Theoretical Computer Science.
Redicolouring digraphs: directed treewidth and cycle-degeneracy
with N. Nisse and I. Sau, in Discrete Applied Mathematics.
Minimum number of arcs in k-critical digraphs with order at most 2𝑘−1
with M. Stiebitz, in Discrete Mathematics.
Digraph redicolouring
with N. Bousquet, F. Havet, N. Nisse, and A. Reinald, in European Journal of Combinatorics.

Strengthening the Directed Brooks' Theorem for oriented graphs and consequences on digraph redicolouring
In Journal of Graph Theory.
Extended abstract in Eurocomb'23.
Unbalanced spanning subgraphs in edge labeled complete graphs
with S. Bessy, J. Pardey, and D. Rautenbach, in The Electronic Journal of Combinatorics.

Factorially Many Maximum Matchings Close to the Erdős-Gallai Bound
with S. Bessy, J. Pardey, and D. Rautenbach, in The Electronic Journal of Combinatorics.
Extended abstract in ICGT 2022.
Complexity of some arc-partition problems for digraphs
with J. Bang-Jensen, S. Bessy, and D. Gonçalves, in Theoretical Computer Science.

An analogue of Reed's conjecture for digraphs
LAMSADE's Discrete Mathematics seminar in Paris, France, 2025.
Graphs@Lyon in Lyon, France, 2025.
GT Graphes et Optimisation in Bordeaux, France, 2024.
National Institute of Informatics in Tokyo, Japan, 2024.
Constrained Flows in Networks
COATI's seminar in Sophia-Antipolis, France, 2024.
Recolouring digraphs of bounded cycle-degeneracy
Third Workshop Complexity and Algorithm (CoA) in Paris, France, 2023.
On the minimum number of arcs in 4-dicritical oriented graphs
WG'23 in Fribourg, Switzerland, 2023.
Fifth ANR Digraph Meeting in Sète, France, 2023.
COATI's seminar in Sophia-Antipolis, France, 2023.
Recolouring digraphs with bounded maximum degree
Group for Discrete Mathematics and Algebra in Ilmenau, Germany, 2024.
PARGO seminar in Fortaleza, Brasil, 2023.
Eurocomb'23 in Prague, Czech Republic, 2023.
Fourth ANR Digraph Meeting in Lyon, France, 2023.
GT Graphes et Optimisation in Bordeaux, France, 2023.
Digraph Redicolouring
Journées Graphes et Algorithmes (JGA) 2022 in Paris, France, 2022.
COATI's seminar in Sophia-Antipolis, France, 2022.
Complexity of some arc-partition problems for digraphs
Journées Graphes et Algorithmes (JGA) 2021 in Montpellier, France, 2021.
COATI's seminar in Sophia-Antipolis, France, 2021.

During my PhD, I was teaching at IUT Université Côte D'Azur.

Introduction aux services réseaux, lecturer (20h), 2024.
Communication et fonctionnement bas niveau, lecturer (26h), 2024.
Méthodes d'optimisation pour l'aide à la décision, teaching assistant (12h), 2024.
Automates et langages, lecturer (6h), 2024.
Automates et langages, teaching assistant (12h), 2023.
Introduction à la programmation, teaching assistant (52h), 2023.
Qualité de développement, lecturer (36h), 2022.
Bases de données avancé, teaching assistant (28h), 2022.

Martin Jouve-Genty, L3, ENS de Lyon.
co-supervised with C. Rambaud and F. Havet, 2024.
Teiki Rigaud, L3, ENS de Paris.
co-supervised with C. Caillouet and F. Havet, 2023.