Jérémie Turcotte

Jérémie Turcotte
McGill University | McGill · Department of Mathematics and Statistics

Master of Science

About

8
Publications
226
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9
Citations

Publications

Publications (8)
Article
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 find all 3-cop-win graphs on 11 vertices, narrow down the possible 4-cop-win graphs on 19 vertices and make some progress on finding the minimum order of 3-cop-win planar g...
Article
We show that the cop number of directed and undirected Cayley graphs on abelian groups is in O(n), where n is the number of vertices, by introducing a refined inductive method. With our method, we improve the previous upper bound on cop number for undirected Cayley graphs on abelian groups, and we establish an upper bound on the cop number of direc...
Article
We prove that the cop number of any 2K2-free graph is at most 2, proving a conjecture of Sivaraman and Testa. We also show that the upper bound of 3 on the cop number of 2K1+K2-free (co-diamond–free) graphs is best possible.
Article
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 connection to complex approximation.
Preprint
We investigate random compact sets with random functions defined thereon, such as polynomials, rational functions, the pluricomplex Green function and the Siciak extremal function. One surprising consequence of our study is that randomness can be used to `improve' convergence for sequences of functions.
Preprint
Full-text available
We show that the cop number of any graph on 18 or fewer vertices is at most 3. This answers a specific case of a question posed by Baird et al. on the minimum order of 4-cop-win graphs, first appearing in 2011. We also find all 3-cop-win graphs on 11 vertices, narrow down the possible 4-cop-win graphs on 19 vertices and get some progress on finding...
Preprint
We prove that the cop number of any $2K_2$-free graph is at most 2, which was previously conjectured by Sivaraman and Testa.
Preprint
Full-text available
We discuss the game of cops and robbers on abelian Cayley graphs. We improve the upper bound for cop number in the undirected case, and we give an upper bound for the directed version. We also construct Meyniel extremal families of graphs with cop number $\Theta (\sqrt{n})$.

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Projects

Project (1)
Project
Various problems on the game of cops and robbers.