Research

Research interests

Most of my research is in Graph Theory, but I am also very interested in problems lying at the intersection of Graph Theory and other areas. In particular, I like concepts related to Geometric Group Theory, Coarse Geometry or Topology.

A few topics I (am trying to) work on: Cayley graphs, coarse graph theory, metric graph theory, cycle bases, geometric group theory, canonical tree-decompositions, twin-width, universal covering, evasiveness of graph properties, fractional colouring of graphs, diameter-degree problem, group tilings.

Preprints

• A coarse Gallai theorem [arXiv]
  Marc Distel, U.G., Jędrzej Hodor, Clément Legrand-Duchesne, Piotr Micek
• Basis Number of Graphs Excluding Minors [arXiv]
  Colin Geniet, U.G.
• Largest planar graphs of diameter 3 and fixed maximum degree – connection with fractional matchings [arXiv]
  Antoine Dailly, Sasha Darmon, U.G., Claire Hilaire, Petru Valicov
• Period-rigidity of one-relator groups [arXiv]
  Solène J. Esnay, U.G., Etienne Moutot

Journal and Conference Publications

• A polynomial bound on the pathwidth of graphs edge-coverable by k shortest paths [arXiv]
  Julien Baste, Lucas De Meyer, U.G., Etienne Objois, Timothé Picavet.
  Short version in STACS 2026.
• Coarse cops and robber in graphs and groups [arXiv]
  Louis Esperet, Harmender Gahlawat, U.G.
  European Journal of Combinatorics, 135 (2026), 104356.
• A note on the structure of locally finite planar quasi-transitive graphs [arXiv]
  U.G.
  The Electronic Journal of Combinatorics, 32(3), P3.50 (2025).
• Periodic colorings and orientations in infinite graphs [arXiv]
  Tara Abrishami, Louis Esperet, U.G., Matthias Hamann, Paul Knappe, Rögnvaldur G. Möller.
  Combinatorial Theory 5(4) (2025)
• Coarse geometry of quasi-transitive graphs beyond planarity [arXiv]
  Louis Esperet, U.G.
  The Electronic Journal of Combinatorics, 31(2), P2.41 (2024).
• Optimization in graphical small cancellation theory [arXiv]
  Louis Esperet, U.G.
  Discrete Mathematics, 347(4) (2024), 113842.
• The structure of quasi-transitive graphs avoiding a minor with applications to the domino problem [arXiv]
  Louis Esperet, U.G., Clément Legrand-Duchesne.
  Short version in Eurocomb 2023.
  Journal version in Journal of Combinatorial Theory, Series B, 169 (2024), 561-613.
• Twin-width V: linear minors, modular counting, and matrix multiplication [arXiv]
  Édouard Bonnet, U.G., Patrice Ossona de Mendez, Stéphan Thomassé.
  Short version in STACS 2023.
• Graphs with convex balls [arXiv]
  Jérémie Chalopin, Victor Chepoi, U.G.
  Geometriae Dedicata, 217 (2023), article number 67.
• Twin-width IV: ordered graphs and matrices [arXiv]
  Édouard Bonnet, U.G., Patrice Ossona de Mendez, Pierre Simon, Stéphan Thomassé, Szymon Toruńczyk.
  Short version in STOC 2022.
  Journal version in Journal of the ACM (2024).

Theses

• Structural and Geometric properties of highly symmetric graphs (PhD thesis) [manuscript]

Talks

Some presentations I gave:

• Cycle bases with low congestion in minor-excluded graphs [slides] [video]
  G-SCOP Grenoble, OC team seminar (2026)
  Discrete Mathematics team seminar, Universität Hamburg (2026)
  Jagiellionian TCS seminar, Uniwersytet Jagielloński, Kraków (2026)
  COATI team seminar, Sofia Antipolis (2026)
  ACRO team seminar, LIS Marseille (2026)
• Structure of graphs edge-coverable by a few isometric paths or trees [slides]
  JGA 2025, IPGP Paris
• Degree-diameter problem in planar graphs of diameter 3 and connection with fractional matchings [slides]
  Open University Discrete Mathematics Seminar (online, 2025)
  10th Cracow Conference on Graph Theory, Kraków (2025)
  ALGCo team seminar, LIRMM Montpellier (2025)
• Structure of quasi-transitive graphs: planarity, minor exclusion and more [slides]
  Seminar Combinatorics and Interactions, Institute of Mathematics of the Polish Academy of Science (2026)
  Séminaire Darboux, Institut Montpelliérain Alexandre Grothendieck (2025)
• Coarse cops and robber games [slides] [video]
  Séminaire Ernest, I2M Marseille (2026)
  Jagiellonian TCS seminar, Uniwersytet Jagielloński, Kraków (2025)
• Coarse geometry of quasi-transitive graphs [slides]
  JGA 2024, Université de Bourgogne, Dijon
  10th Polish Combinatorial Conference (2024)
• Introduction to graph streaming algorithms (for non specialists, in french) [slides]
  Journées CALAMAR 2024 (online)
• Minor exclusion in quasi-transitive graphs [slides] [slides2]
  ESCAPE team seminar (online), LIRMM Montpellier (2026)
  Rauzy Seminar, FRUMAM Marseille (2023)
  JGA 2023, Université Lyon 1
  LoGAlg 2023, Warszawa
  GREYC Caen, Algorithmic seminar (2023)
  G-SCOP Grenoble, OC team seminar (2023)
  Eurocomb 2023, Praha
  Université Paris-Saclay, GALAC team seminar (2023)
  Universität Hamburg, Discrete mathematics team seminar (2023)
• Twin-width V: linear minors, modular counting and matrix multiplication [slides]
  STACS 2023, Hamburg
  JGA 2022, ENS Paris
• Twin-width IV and V: ordered structures, modular counting and matrix multiplication [slides]
  Umeå University, Discrete mathematics team seminar (online, 2023)
  G-SCOP Grenoble, OC team seminar (2023)
• Twin-width IV: ordered graphs and matrices [slides]
  2nd Workshop Complexity and Algorithms, CoA 2022, IHP Paris
• Graphs with convex balls [slides]
  MGT 2021, CIRM Marseille
  JGA 2021 (online)
  LIS Marseille, ACRO team seminar (online) (2021)

You can find [here] my PhD defense’s slides.