Author

Romain Bourneuf

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Preprint Sep 2026

Asymmetric Homomorphism Thresholds for Graphs of Large Odd Girth

We determine the asymmetric homomorphism threshold from graphs of odd girth at least $7$ to triangle-free graphs, showing that $\delta_{\mathrm{hom}}(\{C_3,C_5\},\{C_3\})=\frac{1}{9}$. Equivalently, for every $\varepsilon>0$, every $n$-vertex graph of odd girth at least $7$ and minimum degree at least $(1/9+\varepsilon...

Romain Bourneuf, Raphael Steiner, Stéphan Thomassé et al. · 0 citations

Preprint Sep 2026

The coarse Erd\H{o}s-P\'{o}sa theorem

We prove the coarse Erd\H{o}s-P\'{o}sa conjecture of Georgakopoulos and Papasoglu. Informally, any graph either contains many fat cycles that are pairwise far apart, or there is a small number of bounded radius balls that together hit all of them. To be more precise, if $G$ is a graph with no $q$-fat model of $k \cdot...

Sandra Albrechtsen, Marthe Bonamy, Romain Bourneuf et al. · 0 citations