Vertex colorings of simplicial complexes

Natalia Dobrinskaya; Jesper M. Møller; Dietrich Notbohm

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arXiv · 1007.0710

Vertex colorings of simplicial complexes

Natalia Dobrinskaya·Jesper M. Møller·Dietrich Notbohm

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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.

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BibTeX RIS

Natalia Dobrinskaya, Jesper M. Møller, Dietrich Notbohm. 2010-07-05. Vertex colorings of simplicial complexes. https://arxiv.org/abs/1007.0710

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