Coloring d-embeddable k-uniform hypergraphs
Publikationstyp
Journal Article
Date Issued
2014-10-17
Sprache
English
Institut
TORE-URI
Volume
52
Issue
4
Start Page
663
End Page
679
Citation
Discrete and Computational Geometry 52 (4): 663-679 (2014)
Publisher DOI
Scopus ID
Publisher
Springer
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.).
Subjects
Chromatic number
Coloring
Embeddings
Four Color Theorem
Hypergraphs
DDC Class
510: Mathematik