Chromatic Numbers of Algebraic Hypergraphs
Logic
2015-11-09 v4
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.
Cite
@article{arxiv.1408.4716,
title = {Chromatic Numbers of Algebraic Hypergraphs},
author = {James H. Schmerl},
journal= {arXiv preprint arXiv:1408.4716},
year = {2015}
}
Comments
This 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