Homotopy theory of graphs
By Eric K. Babson, H. Barcelo, M. Longueville, Reinhard C. Laubenbacher. 2004
114 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6fe94f61d11e7d5f6d9cb8c8cd071adc72180c1f
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In Computational Theory and Mathematics
In Discrete Mathematics and Combinatorics
In Mathematical Physics
- Shing-Tung Yau
- Alexander Grigorʼyan
- Yuri V. Muranov
- Alexander Grigor yan
- Yong Lin
- Valerio Capraro
- Valentino Tosatti
- Martin T. Barlow
Citations in the corpus
- Homologies of digraphs and Künneth formulas (2017, background): “Secondly, there is an independently developed notion of homotopy of digraphs [10] (similar to homotopy theory on graphs [1], [3]) that is compatible with path homology.”
- Cohomology of digraphs and (undirected) graphs (2015, methodology): “Thus we transfer the cohomology theory to the category of graphs and prove it is homotopy invariant in relation to the homotopy theory defined in [1] and [2].”
- Homotopy theory for digraphs (2014, background): “(f)◦π1 (g) is an isomorphism of π1 (S3) ≃Z onto itself, which is not possible by π1 (G∗) = {0}. 6 Homology and homotopy of (undirected)graphs A homotopy theory of undirected graphs was constructed in [1] and [2] (see also [4]). Here we show that this theory can be obtained from our homotopy theory o”
- Discrete homology theory for metric spaces (2013, background): “Alternatively, discrete homotopy theory is defined as a cubical homotopy theory in [3].”