Author

James Davies

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Preprint Sep 2026

Hadwiger--Nelson Problem for Typical Norms

The classical Hadwiger-Nelson problem asks for the chromatic number of the unit distance graph of the Euclidean plane. Over the years, this problem has been considered for a variety of other normed spaces, with higher-dimensional Euclidean space $\mathbb{R}^d$ being perhaps the most natural and well-studied. Alon, Buci...

Noga Alon, Matija Bucic, James Davies · 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