A Homotopy Theory for Graphs
Combinatorics
2007-05-23 v1
Abstract
The recently introduced A-homotopy groups for graphs are investigated. The main concern of the present article is the construction of an infinite cell complex, the homotopy groups of which are isomorphic to the A-homotopy groups of the given graph. We present a natural candidate for such a cell complex, together with a homomorphism between the corresponding groups that indeed yields an isomorphism, if a cubical analog of the simplicial approximation theorem holds, which - so far - we were unable to prove.
Cite
@article{arxiv.math/0403146,
title = {A Homotopy Theory for Graphs},
author = {E. Babson and H. Barcelo and M. de Longueville and R. Laubenbacher},
journal= {arXiv preprint arXiv:math/0403146},
year = {2007}
}
Comments
11 pages, 3 figures