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Graph homotopy and Graham homotopy

Beifang Chen Shing-Tung Yau Yeong-Nan Yeh

Convex and Discrete Geometry mathscidoc:1912.43524

Discrete Mathematics, 241, 153-170, 2001.10
Simple-homotopy for cell complexes is a special type of topological homotopy constructed by elementary collapses and elementary expansions. In this paper, we introduce graph homotopy for graphs and Graham homotopy for hypergraphs and study the relation between the two homotopies and the simple-homotopy for cell complexes. The graph homotopy is useful to describe topological properties of discretized geometric figures, while the Graham homotopy is essential to characterize acyclic hypergraphs and acyclic relational database schemes.
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@inproceedings{beifang2001graph,
  title={Graph homotopy and Graham homotopy},
  author={Beifang Chen, Shing-Tung Yau, and Yeong-Nan Yeh},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203815466139088},
  booktitle={Discrete Mathematics},
  volume={241},
  pages={153-170},
  year={2001},
}
Beifang Chen, Shing-Tung Yau, and Yeong-Nan Yeh. Graph homotopy and Graham homotopy. 2001. Vol. 241. In Discrete Mathematics. pp.153-170. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203815466139088.
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