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.

Email: lpicasarr@nii.ac.jp

On the number of maximal independent sets in 𝑲₄-free graphs
with T. Hartel and D. Rautenbach.
Acyclic dichromatic number of oriented graphs
with J. Bang-Jensen and A. Yeo.
On cuts of small chromatic number in sparse graphs
with G. Aubian, M. Bonamy, R. Bourneuf, and O. Fontaine.
Generalized DP-colorings of digraphs
with M. Stiebitz.
The complexity of finding and counting subtournaments
with S. Döring, S. Houdaigoui, and P. Wellnitz.
Chromatic discrepancy of locally 𝑠-colourable graphs
with T. Corsini, T. Pierron, F. Pirot, and E. Robinson.
(𝚫−1)-dicolouring of digraphs
with A. Harutyunyan, K. Kawarabayashi, and G. Puig i Surroca.
Edge-colouring and orientations: applications to degree-boundedness and 𝛘-boundedness
with A. Char and K. Kawarabayashi.
Blow-ups and extensions of trees in tournaments
with P. Aboulker, F. Havet, W. Lochet, R. Lopes, and C. Rambaud.

Backbone colouring of chordal graphs
with J. Araújo and N. Nisse, in the proceedings of LAGOS 2025.
Brooks-type colourings of digraphs in linear time
with D. Gonçalves and A. Reinald, in Journal of Graph Theory.
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.

Chromatic discrepancy of locally 𝑠-colourable graphs
NII's lunch seminar, Tokyo, 2025.
Journées Graphes et Algorithmes, Paris, 2025.
(𝚫−1)-dicolouring of digraphs
Imada's seminar, Odense, 2025.
An analogue of Reed's conjecture for digraphs
LAMSADE's Discrete Mathematics seminar, Paris, 2025.
Graphs@Lyon's seminar, Lyon, 2025.
SODA 2025, New Orleans, 2025.
GT Graphes et Optimisation's seminar, Bordeaux, 2024.
NII's lunch seminar, Tokyo, 2024.
Blow-ups and extensions of trees in tournaments
NII's lunch seminar, Tokyo, 2024.
Constrained Flows in Networks
COATI's seminar, Sophia-Antipolis, 2024.
Recolouring digraphs of bounded cycle-degeneracy
Third Workshop Complexity and Algorithm, Paris, 2023.
On the minimum number of arcs in 4-dicritical oriented graphs
WG'23, Fribourg, 2023.
Fifth ANR Digraph Meeting, Sète, 2023.
COATI's seminar, Sophia-Antipolis, 2023.
Recolouring digraphs with bounded maximum degree
Group for Discrete Mathematics and Algebra's seminar, Ilmenau, 2024.
PARGO's seminar, Fortaleza, 2023.
Eurocomb'23, Prague, 2023.
Fourth ANR Digraph Meeting, Lyon, 2023.
GT Graphes et Optimisation's seminar, Bordeaux, 2023.
Digraph Redicolouring
Journées Graphes et Algorithmes, Paris, 2022.
COATI's seminar, Sophia-Antipolis, 2022.
Complexity of some arc-partition problems for digraphs
Journées Graphes et Algorithmes, Montpellier, 2021.
COATI's seminar, Sophia-Antipolis, 2021.

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

Introduction aux services réseaux, lecturer (22h), 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.

Samuel Coulomb
Colouring digraphs with bounded maximum degree.
Research Internship, Master 2, ENS de Paris, May - September 2025.
Co-supervised with K. Kawarabayashi.
Martin Jouve-Genty
Erdős-Pósa properties for small cycles in digraphs.
Research Internship, Licence 3, ENS de Lyon, June - July 2024.
Co-supervised with C. Rambaud and F. Havet.
Teiki Rigaud
A scheduling problem for LoRa technology.
Research Internship, Licence 3, ENS de Paris, June - July 2023.
Co-supervised with C. Caillouet and F. Havet.