4 papers
Noncommutative properties of 0-hyperbolic graphs
Amaury Freslon, Paul Meunier, Pegah Pournajafi
We study several noncommutative properties of 0-hyperbolic graphs. In particular, we prove that 0-hyperbolicity is preserved under quantum isomorphism. We also compute the quantum…
Block structures of graphs and quantum isomorphism
Amaury Freslon, Paul Meunier, Pegah Pournajafi
We prove that for every pair of quantum isomorphic graphs, their block trees and their block graphs are isomorphic, and that such an isomorphism can be chosen so that the correspon…
Vertex gluing preserves the bunkbed conjecture
Paul Meunier, Pegah Pournajafi
We prove that the bunkbed conjecture is preserved under gluing along a vertex. As a consequence, every minimal counterexample is 2-connected. More generally, for any class of graph…
Quantum properties of -cographs
Paul Meunier
We initiate a systematic study of quantum properties of finite graphs, namely, quantum asymmetry, quantum symmetry, and quantum isomorphism. We define the Schmidt alternative for a…