# Osthus, Deryk

## Simultaneous partition of hypergraphs ★★

**Problem**Let and be two -uniform hypergraph on the same vertex set . Does there always exist a partition of into classes such that for both , at least hyperedges of meet each of the classes ?

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## Complexity of the H-factor problem. ★★

An -factor in a graph is a set of vertex-disjoint copies of covering all vertices of .

**Problem**Let be a fixed positive real number and a fixed graph. Is it NP-hard to determine whether a graph on vertices and minimum degree contains and -factor?

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