Vertex colorings of simplicial complexes

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.

References in corpus (3)

• Triangulated Manifolds with Few Vertices: Centrally Symmetric Spheres and Products of Spheres
• Colorings of simplicial complexes and vector bundles over Davis-Januszkiewicz spaces
• Vector bundles over Davis-Januszkiewicz spaces with prescribed characteristic classes