13 papers
Faithful universal graphs for minor-closed classes
Paul Bastide, Louis Esperet, Carla Groenland +3
It was proved by Huynh, Mohar, Šámal, Thomassen and Wood in 2021 that any countable graph containing every countable planar graph as a subgraph has an infinite clique minor. We p…
Antifactors in bipartite multigraphs
Louis Esperet
Let be a -regular bipartite graph with bipartition . It was proved by Lu, Wang, and Yan in 2020 that has a spanning subgraph such that each vertex of has…
Multiparty equality in the local broadcast model
Louis Esperet, Jean-Florent Raymond
In this paper we consider the multiparty equality problem in graphs, where every vertex of a graph is given an input, and the goal of the vertices is to decide whether all inpu…
Local certification of geometric graph classes
Oscar Defrain, Louis Esperet, Aurélie Lagoutte +2
The goal of local certification is to locally convince the vertices of a graph that satisfies a given property. A prover assigns short certificates to the vertices of the g…
Cops and robber in graphs with bounded vertex cover number
Prosenjit Bose, Louis Esperet, JÄdrzej Hodor +3
Meyniel's conjecture states that -vertex connected graphs have cop number . The current best known upper bound is , proved independentl…
Coarse cops and robber in graphs and groups
Louis Esperet, Harmender Gahlawat, Ugo Giocanti
(abstract shortened to meet arxiv's length requirements) We investigate two variants of the classical Cops and robber game in graphs, recently introduced by Lee, MartÃnez-Pedroza,…