Publisher DOI: 10.1007/s00454-014-9641-2
Title: Coloring d-embeddable k-uniform hypergraphs
Language: English
Authors: Heise, Carl Georg 
Panagiotou, Konstantinos 
Pikhurko, Oleg 
Taraz, Anusch 
Keywords: Chromatic number;Coloring;Embeddings;Four Color Theorem;Hypergraphs
Issue Date: 17-Oct-2014
Publisher: Springer
Source: Discrete and Computational Geometry 52 (4): 663-679 (2014)
Abstract (english): 
This 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.).
URI: http://hdl.handle.net/11420/9901
ISSN: 1432-0444
Institute: Mathematik E-10 
Document Type: Article
Journal: Discrete & computational geometry 
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