title: Coloring [Formula: see text]-Embeddable [Formula: see text]-Uniform Hypergraphs.
abstract: 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].
authors.affiliation: Institut für Mathematik, Technische Universität Hamburg-Harburg, Hamburg, Germany.
authors.forename: Carl Georg
authors.initials: CG
authors.lastname: Heise
authors.affiliation: Mathematisches Institut, Ludwig-Maximilians-Universität München, Munich, Germany.
authors.forename: Konstantinos
authors.initials: K
authors.lastname: Panagiotou
authors.affiliation: Mathematics Institute and DIMAP, University of Warwick, Coventry, UK.
authors.forename: Oleg
authors.initials: O
authors.lastname: Pikhurko
authors.affiliation: Institut für Mathematik, Technische Universität Hamburg-Harburg, Hamburg, Germany.
authors.forename: Anusch
authors.initials: A
authors.lastname: Taraz
keywords:  Four Color Theorem; Chromatic number; Coloring; Embeddings; Hypergraphs