Let $G$ be an $r$-uniform hypergraph. When is it possible to orient the edgesof $G$ in such a way that every $p$-set of vertices has some $p$-degree equalto $0$? (The $p$-degrees generalise for sets of vertices what in-degree andout-degree are for single vertices in directed graphs.) Caro and Hansberg askedif the obvious Hall-type necessary condition is also sufficient. Our main aim is to show that this is true for $r$ large (for given $p$), butfalse in general. Our counterexample is based on a new technique in sparseRamsey theory that may be of independent interest.
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机译：令$ G $为$ r $一致的超图。什么时候可以使$ G $的边沿这样定向，使得每个$ p $-个顶点集具有一定的$ p $-度等于$ 0 $？ （$ p $ -degrees表示一组顶点，有向图和out-degree表示有向图中的单个顶点。）Caro和Hansberg询问明显的霍尔型必要条件是否也足够。我们的主要目的是证明对于大的$ r $（对于给定的$ p $）这是正确的，但通常是false。我们的反例基于sparseRamsey理论中的一种新技术，该技术可能具有独立的意义。
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