A Homotopy Theory for Graphs

Details A Homotopy Theory for Graphs A Homotopy Theory for Graphs

2004-03-09

arxiv.org/abs/math/0403146v1

Mathematics

Combinatorics

11 pages, 3 figures

Scientific paper

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.

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