Heise, Carl GeorgCarl GeorgHeisePanagiotou, KonstantinosKonstantinosPanagiotouPikhurko, OlegOlegPikhurkoTaraz, AnuschAnuschTaraz2021-07-152021-07-152014-10-17Discrete and Computational Geometry 52 (4): 663-679 (2014)http://hdl.handle.net/11420/9901This paper extends the scenario of the Four Color Theorem in the following way. Let Hd,k be the set of all k-uniform hypergraphs that can be (linearly) embedded into Rd. We investigate lower and upper bounds on the maximum (weak) chromatic number of hypergraphs in Hd,k. For example, we can prove that for (Formula presented.) there are hypergraphs in H2d-3,d on n vertices whose chromatic number is Ω(log n/log log n), whereas the chromatic number for n-vertex hypergraphs in Hd,d is bounded by (Formula presented.).en1432-044420144663679SpringerChromatic numberColoringEmbeddingsFour Color TheoremHypergraphsMathematikJournal Article10.1007/s00454-014-9641-2Other