Chromatic Numbers of Algebraic Hypergraphs
arXiv:1408.4716
Abstract
A k-uniform hypergraph is algebraic if its vertex set is n-dimensional Euclidean space, for some n, and its hyperedge set is defined from the zero set of some polynomial. The chromatic numbers of all algebraic hypergraphs are determined, provided they are infinite.
arXiv commentThis version has been completely rewritten. The most important change is the elimination of Sections 3 and 4 since the proof Theorem 3.1 had some flaws that resisted repairs. It is hoped that Theorem 3.1 will reappear in the future