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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

Spanning subhypergraphs with degree constraints

An old result of Tutte states that any $d$-regular graph contains a spanning subgraph in which every vertex has degree $k$ or $k+1$, for every $1\leq k\leq d$. We generalize this statement to hypergraphs, showing, for example, that every $3$-uniform $d$-regular hypergraph contains a subgraph in which all degrees are $k...

Noga Alon, P. Haxell, Aleksa Milojević et al. · 0 citations

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