We prove that every finite set of homothetic copies of a given convex body in the plane can be colored with four colors so that any point covered by at least two copies is covered by two copies with distinct colors. This generalizes a previous result from Smorodinsky (SIAM J. Disc. Math. 2007). Then we show that for any k≥2, every three-dimensional hypergraph can be colored with 6(k-1) colors so that every hyperedge e contains min{
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机译：我们证明给定凸体在平面上的每组有限数量的同类副本可以用四种颜色着色，以便至少两个副本覆盖的任何点都可以被两个具有不同颜色的副本覆盖。这概括了Smorodinsky的先前结果（SIAM J. Disc。Math。2007）。然后我们证明，对于任何k≥2，每个三维超图都可以用6（k-1）种颜色着色，从而每个超边e都包含min {
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