13 citations · 36 across the 13 of their papers we have counts for
13 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…
Finding dense minors using average degree
Kevin Hendrey, Sergey Norin, Raphael Steiner +1
Motivated by Hadwiger's conjecture, we study the problem of finding the densest possible -vertex minor in graphs of average degree at least . We show that if has averag…
Limits of degeneracy for colouring graphs with forbidden minors
Sergey Norin, Jérémie Turcotte
Motivated by Hadwiger's conjecture, Seymour asked which graphs have the property that every non-null graph with no minor has a vertex of degree at most . We s…
Improved bounds on the cop number when forbidding a minor
Franklin Kenter, Erin Meger, Jérémie Turcotte
Andreae (1986) proved that the cop number of connected -minor-free graphs is bounded for every graph . In particular, the cop number is at most if contains n…
Cops and robbers on -free graphs
Maria Chudnovsky, Sergey Norin, Paul Seymour +1
We prove that every connected -free graph has cop number at most two, solving a conjecture of Sivaraman. In order to do so, we first prove that every connected -free grap…
The Burning Number Conjecture Holds Asymptotically
Sergey Norin, Jérémie Turcotte
The burning number of a graph is the smallest number of turns required to burn all vertices of a graph if at every turn a new fire is started and existing fires spread t…
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.…
4-cop-win graphs have at least 19 vertices
Jérémie Turcotte, Samuel Yvon
We show that the cop number of any graph on 18 or fewer vertices is at most 3. This answers a question posed by Andreae in 1986, as well as more recently by Baird et al. We also fi…
Cops and robbers on -free graphs
Jérémie Turcotte
We prove that the cop number of any -free graph is at most 2, proving a conjecture of Sivaraman and Testa. We also show that the upper bound of on the cop number of $2K_1…
Cops and robbers on directed and undirected abelian Cayley graphs
Peter Bradshaw, Seyyed Aliasghar Hosseini, Jérémie Turcotte
We show that the cop number of directed and undirected Cayley graphs on abelian groups has an upper bound of the form of , where is the number of vertices, by intr…
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…