5 papers
Longest cycles in vertex-transitive and highly connected graphs
Carla Groenland, Sean Longbrake, Raphael Steiner +2
We present progress on three old conjectures about longest paths and cycles in graphs. The first pair of conjectures, due to Lovász from 1969 and Thomassen from 1978, respectively,…
Twin-width of sparse random graphs
Kevin Hendrey, Sergey Norin, Raphael Steiner +1
We show that the twin-width of every -vertex -regular graph is at most and that almost all -regular graphs attain this bound. More generally, w…
On an induced version of Menger's theorem
Kevin Hendrey, Sergey Norin, Raphael Steiner +1
We prove Menger-type results in which the obtained paths are pairwise non-adjacent, both for graphs of bounded maximum degree and, more generally, for graphs excluding a topologica…
Approximation by random complex polynomials and random rational functions
Paul M. Gauthier, Thomas Ransford, Simon St-Amant +1
We investigate random compact sets with random functions defined thereon, such as polynomials, rational functions, the pluricomplex Green function and the Siciak extremal function.…
Approximation by random complex polynomials and rational functions
Simon St-Amant, Jérémie Turcotte
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in conne…