Bio
As of August 2024, I will be a postdoctoral fellow 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.
Contact
lucas.picasarri-arrieta@inria.fr
Bat. Lagrange, Office L010C,
Inria Sophia Antipolis Méditerranée,
2004 route des Lucioles,
06902 Sophia Antipolis, France
Publications
Preprints
- An analogue of Reed's conjecture for digraphs
with K. Kawarabayashi, 2024. - Brooks-type colourings of digraphs in linear time
with D. Gonçalves and A. Reinald, 2024. - The 3-dicritical semi-complete digraphs
with F. Havet and F. Hörsch, 2024. - Complexity results on the decomposition of a digraph into directed linear forests and out-stars
with F. Hörsch, 2024. - Dichromatic number of chordal graphs
with S. Bessy and F. Havet, 2023.
- On the minimum number of arcs in 4-dicritical oriented graphs
with F. Havet and C. Rambaud, to appear in Journal of Graph Theory, 2024. - Subdivisions in dicritical digraphs with large order or digirth
with C. Rambaud, in European Journal of Combinatorics, 2024, available on ArXiv. - Constrained Flows in Networks
with S. Bessy and J. Bang-Jensen, in Theoretical Computer Science, 2024, available on ArXiv. - Redicolouring digraphs: directed treewidth and cycle-degeneracy
with N. Nisse and I. Sau, in Discrete Applied Mathematics, 2024, available on ArXiv. - Minimum number of arcs in k-critical digraphs with order at most 2k−1
with M. Stiebitz, in Discrete Mathematics, 2024, available on ArXiv. - Digraph redicolouring
with N. Bousquet, F. Havet, N. Nisse, and A. Reinald, in European Journal of Combinatorics, 2024, available on ArXiv. - Strengthening the Directed Brooks' Theorem for oriented graphs and consequences on digraph redicolouring
in Journal of Graph Theory, 2023, available on ArXiv. - Unbalanced spanning subgraphs in edge labeled complete graphs
with S. Bessy, J. Pardey, and D. Rautenbach, in Electronic Journal of Combinatorics, 2023, available on ArXiv. - Factorially Many Maximum Matchings Close to the Erdős-Gallai Bound
with S. Bessy, J. Pardey, and D. Rautenbach, in Electronic Journal of Combinatorics, 2022, available on ArXiv. - Complexity of some arc-partition problems for digraphs
with J. Bang-Jensen, S. Bessy, and D. Gonçalves, in Theoretical Computer Science, 2022, available on HAL.
- Strengthening the Directed Brooks' Theorem for oriented graphs and consequences on digraph redicolouring
Eurocomb'23. - On the minimum number of arcs in 4-dicritical oriented graphs
with F. Havet and C. Rambaud, in the proceedings of WG'23.
Talks
- Constrained Flows in Networks
For the COATI seminar in Sophia-Antipolis, France, 2024. - Recolouring digraphs of bounded cycle-degeneracy
For the Third Workshop Complexity and Algorithm (CoA) in Paris, France, 2023. - On the minimum number of arcs in 4-dicritical oriented graphs
For the Fifth ANR Digraph Meeting in Sète, France, 2023.
For the COATI seminar in Sophia-Antipolis, France, 2023. - Recolouring digraphs with bounded maximum degree
For the Group for Discrete Mathematics and Algebra in Ilmenau, Germany, 2024.
For the PARGO seminar in Fortaleza, Brasil, 2023.
For the Fourth ANR Digraph Meeting in Lyon, France, 2023.
For the GT Graphes et Optimisation in Bordeaux, France, 2023. - Digraph Redicolouring
For the Journées Graphes et Algorithmes (JGA) 2022 in Paris, France, 2022.
For the COATI seminar in Sophia-Antipolis, France, 2022. - Complexity of some arc-partition problems for digraphs
For the Journées Graphes et Algorithmes (JGA) 2021 in Montpellier, France, 2021.
For the COATI seminar in Sophia-Antipolis, France, 2021.
Teaching
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.
Student supervision
- Martin Jouve-Genty, L3, ENS de Lyon.
co-supervised with C. Rambaud, 2024. - Teiki Rigaud, L3, ENS de Paris.
co-supervised with C. Caillouet and F. Havet, 2023.