Guillaume Lecomte

collaborators

6 papers

math.GR2026

Eventual Exactness and Rigidity for Abelian Covers of Groups

Guillaume Lecomte

For a group $G$ , let $a (G)$ denote the minimum number of abelian subgroups covering $G$ , and let $ω (G)$ be the maximum size of a pairwise noncommuting set. We prove the exact formu…

math.CO2026

An improved lower bound for the blowup defective chromatic separation constant

Guillaume Lecomte

For a graph $G$ and an integer $d \geq 0$ , let $χ^{d} (G)$ denote the $d$ -defective chromatic number, and let $G ⊠ K_{d + 1}$ be the $(d + 1)$ -fold clique blowup of $G$ . Norin and…

math.GR2026

Sharp Asymptotics for Abelian Covers of Groups with Bounded Noncommutativity

Guillaume Lecomte

We determine the sharp exponential growth rate of the minimum number of abelian subgroups required to cover a group with bounded pairwise noncommutativity. Let $ω (G)$ denote the la…

math.CO2026

Connected Counterexamples for Target Ramsey Numbers

Guillaume Lecomte

Chartrand and Zhang asked whether there exists a graph $G$ without isolated vertices whose target Ramsey number satisfies $TR (G) > R (G)$ . We answer the question a…

math.OC2026

The Certification Limits of KS-Type Layer Relaxations: A Square-Root Ceiling and Its Breakdown

Guillaume Lecomte

A separable bilinear layer relaxation assigns a population cost to each layer and a nonpositive bilinear coupling to each pair of layers, then excludes a profile span whenever the…

math.OC2026

A certified refinement and asymptotic analysis of the Kuznetsov-Sahinidis diameter bound for Lennard-Jones clusters

Guillaume Lecomte

Kuznetsov and Sahinidis (J. Glob. Optim., 2025) prove distance bounds that confine optimal Lennard-Jones clusters and shrink the search region of deterministic solvers; their diame…