Coloring [Formula: see text] -Embeddable [Formula: see text] -Uniform Hypergraphs

This paper extends the scenario of the Four Color Theorem in the following way. Let [Formula: see text] be the set of all [Formula: see text] -uniform hypergraphs that can be (linearly) embedded into [Formula: see text] . We investigate lower and upper bounds on the maximum (weak) chromatic number o...

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Detalles Bibliográficos
Autores principales: Heise, Carl Georg, Panagiotou, Konstantinos, Pikhurko, Oleg, Taraz, Anusch
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2014
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4237724/
https://www.ncbi.nlm.nih.gov/pubmed/25419024
http://dx.doi.org/10.1007/s00454-014-9641-2
Descripción
Sumario:This paper extends the scenario of the Four Color Theorem in the following way. Let [Formula: see text] be the set of all [Formula: see text] -uniform hypergraphs that can be (linearly) embedded into [Formula: see text] . We investigate lower and upper bounds on the maximum (weak) chromatic number of hypergraphs in [Formula: see text] . For example, we can prove that for [Formula: see text] there are hypergraphs in [Formula: see text] on [Formula: see text] vertices whose chromatic number is [Formula: see text] , whereas the chromatic number for [Formula: see text] -vertex hypergraphs in [Formula: see text] is bounded by [Formula: see text] for [Formula: see text] .

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