Bertille Granet

activity

20192026

most citedPath and cycle decompositions of dense graphs

6 citations · 11 across the 9 of their papers we have counts for

collaborators

10 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 $δ_{C_{ℓ}}$ i…

math.CO2026

On $2$ -factors of Hamiltonian graphs

Alberto Espuny Díaz, António Girão, 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…

math.CO2024

Hitting times in the binomial random graph

Bertille Granet, Felix Joos, Jonathan Schrodt

Fix $k \geq 2$ , choose $\frac{l o g n}{n ^{(k - 1) / k}} \leq p \leq 1 - Ω (\frac{l o g ^{4} n}{n})$ , and consider $G \sim G (n, p)$ . For any pair of vertices $v, w \in V (G)$ , we give a simple and prec…

math.CO2024

Seymour's second neighbourhood conjecture: random graphs and reductions

Alberto Espuny Díaz, António Girão, Bertille Granet +1

A longstanding conjecture of Seymour states that in every oriented graph there is a vertex whose second outneighbourhood is at least as large as its outneighbourhood. In this short…

math.CO2023★ 3 cited

Random perfect matchings in regular graphs

Bertille Granet, Felix Joos

We prove that in all regular robust expanders $G$ every edge is asymptotically equally likely contained in a uniformly chosen perfect matching $M$ . We also show that given any fixe…

math.CO2022

Hamilton decompositions of regular bipartite tournaments

Bertille Granet

A regular bipartite tournament is an orientation of a complete balanced bipartite graph $K_{2 n, 2 n}$ where every vertex has its in- and outdegree both equal to $n$ . In 1981, Jackson…

math.CO2020★ 2 cited

Path decompositions of tournaments

António Girão, Bertille Granet, Daniela Kühn +2

In 1976, Alspach, Mason, and Pullman conjectured that any tournament $T$ of even order can be decomposed into exactly $ex (T)$ paths, where ${\rm ex}(T):= \frac{1}{2}\sum_{v\i…

math.CO2019★ 6 cited

Path and cycle decompositions of dense graphs

António Girão, Bertille Granet, Daniela Kühn +1

We make progress on three long standing conjectures from the 1960s about path and cycle decompositions of graphs. Gallai conjectured that any connected graph on $n$ vertices can be…

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

Hitting times in the binomial random graph

Seymour's second neighbourhood conjecture: random graphs and reductions

Random perfect matchings in regular graphs

Hamilton decompositions of regular bipartite tournaments

Path decompositions of tournaments

Path and cycle decompositions of dense graphs

On $2$ -factors of Hamiltonian graphs