Simplicial simplehomotopy of flag complexes in terms of graphs
Abstract
A flag complex can be defined as a simplicial complex whose simplices correspond to complete subgraphs of its 1skeleton taken as a graph. In this article, by introducing the notion of sdismantlability, we shall define the shomotopy type of a graph and show in particular that two finite graphs have the same shomotopy type if, and only if, the two flag complexes determined by these graphs have the same simplicial simplehomotopy type (Theorem 2.10, part 1). This result is closely related to similar results established by Barmak and Minian (Adv. in Math., 218 (2008), 87104) in the framework of posets and we give the relation between the two approaches (theorems 3.5 and 3.7). We conclude with a question about the relation between the shomotopy and the graph homotopy defined by Chen, Yau and Yeh (Discrete Math., 241(2001), 153170).
 Publication:

arXiv eprints
 Pub Date:
 September 2008
 arXiv:
 arXiv:0809.1751
 Bibcode:
 2008arXiv0809.1751B
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Algebraic Topology
 EPrint:
 15 pages, 8 figures (in tex format