Guillaume Lecomte

Sharp Asymptotics for Abelian Covers of Groups with Bounded Noncommutativity

We determine the sharp exponential growth rate of the minimum number of abelian subgroups required to cover a group with bounded pairwise noncommutativity. Let omega(G) denote the largest size of a pairwise noncommuting subset of a group G, let a(G) be the least size of an abelia...

Sharp Asymptotics for Abelian Covers of Groups with Bounded Noncommutativity

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 largest size of a pairwise noncommuting subset of a group G, let a(G) be the least size of an abelian co...

Sharp Asymptotics for Abelian Covers of Groups with Bounded Noncommutativity

We determine the sharp exponential growth rate of the minimum number of abelian subgroups required to cover a group with bounded pairwise noncommutativity. Let omega(G) denote the largest size of a pairwise noncommuting subset of a group G, let a(G) be the least size of an abelia...

Sharp Asymptotics for Abelian Covers of Groups with Bounded Noncommutativity

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 largest size of a pairwise noncommuting subset of a group G, let a(G) be the least size of an abelian co...

Connected Counterexamples for Target Ramsey Numbers

We answer an open problem of Chartrand and Zhang concerning target Ramsey numbers. We prove that there exist infinitely many connected graphs whose target Ramsey number is strictly larger than their ordinary Ramsey number. The proof combines an elementary counting lower bound wit...