Author

P. Haxell

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Preprint Oct 2026

The chromatic number of $G$-stable Kneser graphs

Extending the notions of Kneser graphs and Schrijver graphs, we define the $G$-stable Kneser graph $KG(G,k)$ (where $k\geq 2$ and $G$ is a graph on $n\geq 2k$ vertices) as the graph whose vertices are the $k$-element independent sets in $G$ and whose edges join pairs of disjoint independent sets. The well-known result...

C. Arana, P. Haxell, Tomáš Kaiser et al. · 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