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, geometric group theory, canonical tree-decompositions, twin-width, universal covering, evasiveness of graph properties, fractional colouring of graphs, diameter-degree problem, group tilings.

Preprints

• 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
• Coarse cops and robber in graphs and groups [arXiv]
  Louis Esperet, Harmender Gahlawat, U.G.
• Period-rigidity of one-relator groups [arXiv]
  Solène J. Esnay, U.G., Etienne Moutot

Journal and Conference Publications

• A note on the structure of locally finite planar quasi-transitive graphs [arXiv]
  U.G.
  The Electronic Journal of Combinatorics (to appear)
• Periodic colorings and orientations in infinite graphs [arXiv]
  Tara Abrishami, Louis Esperet, U.G., Matthias Hamann, Paul Knappe, Rögnvaldur G. Möller.
  Combinatorial Theory (to appear)
• 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:

• Degree-diameter problem in planar graphs of diameter 3 and connection with fractional matchings [slides]
  ALGCo team seminar, LIRMM Montpellier (2025)
• Structure of quasi-transitive graphs: planarity, minor exclusion and more [slides]
  Séminaire Darboux, Institut Montpelliérain Alexandre Grothendieck (2025)
• Coarse cops and robber games [slides] [video]
  Jagellonian 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]
  Rauzy Seminar, FRUMAM Marseille (2023)
  JGA 2023, Université Lyon 1
  LoGAlg 2023, Warsawa
  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.