# Graph homotopy and Graham homotopy

@article{Chen2001GraphHA, title={Graph homotopy and Graham homotopy}, author={Beifang Chen and Shing-Tung Yau and Yeong-Nan Yeh}, journal={Discrete Mathematics}, year={2001}, volume={241}, pages={153-170} }

Abstract 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… CONTINUE READING

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