Vertex colorings of simplicial complexes
Algebraic Topology
2010-10-18 v1 Combinatorics
Abstract
We define an (r,s)-coloring of an abstract simplicial complex to be a coloring using r colors of the vertices so that in any simplex at most s vertices have the same color. We translate the problem of finding an (r,s)-coloring of a given simplex to a topological problem and to a ring theoretic problem. The topological version involves vector bundles over Davis--Januszkiewicz spaces and the algebraic one involves factorizations in Stanley-Reisner rings.
Keywords
Cite
@article{arxiv.1007.0710,
title = {Vertex colorings of simplicial complexes},
author = {Natalia Dobrinskaya and Jesper M. Møller and Dietrich Notbohm},
journal= {arXiv preprint arXiv:1007.0710},
year = {2010}
}