Bertille Granet

collaborators

4 papers

math.CO2026

Determining decomposition thresholds for long odd cycles

Bertille Granet, Daniel Horsley

An $ℓ$ -cycle decomposition of a graph $G$ is a set of $ℓ$ -cycles in $G$ whose edge sets partition the edge set of $G$ . The $ℓ$ -cycle decomposition threshold $I^´_{C_{ℓ}}$ …

math.CO2026

On $2$ -factors of Hamiltonian graphs

Alberto Espuny DÃaz, AntÃ³nio GirÃ£o, Bertille Granet +1

Let $k \geq 2$ . We show that, for a sufficiently small $ε > 0$ , any sufficiently large $n$ -vertex Hamiltonian graph of minimum degree at least $n^{1 - ε}$ contains a…

math.CO2026

Compatible Hamilton cycles in graphs with large minimum degree

Natalie Behague, Francesco Di Braccio, Bertille Granet +1

The renowned theorem of Dirac states that if $G$ is a graph with minimum degree at least $n /2$ then $G$ has a Hamilton cycle. A natural generalisation asks what properties of an ed…

math.CO2025

The semi-inducibility problem

Abdul Basit, Bertille Granet, Daniel Horsley +2

Let $H$ be a $k$ -edge-coloured graph and let $n$ be a positive integer. What is the maximum number of copies of $H$ in a $k$ -edge-coloured complete graph on $n$ vertices? This pape…

Determining decomposition thresholds for long odd cycles

On 2-factors of Hamiltonian graphs

Compatible Hamilton cycles in graphs with large minimum degree

The semi-inducibility problem

On $2$ -factors of Hamiltonian graphs