  A flag complex can be defined as a simplicial complex whose simplices
correspond to complete subgraphs of its 1-skeleton taken as a graph. In this
article, by introducing the notion of s-dismantlability, we shall define the
s-homotopy type of a graph and show in particular that two finite graphs have
the same s-homotopy type if, and only if, the two flag complexes determined by
these graphs have the same simplicial simple-homotopy type (Theorem 2.10, part
1). This result is closely related to similar results established by Barmak and
Minian (Adv. in Math., 218 (2008), 87-104) 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 s-homotopy and the
graph homotopy defined by Chen, Yau and Yeh (Discrete Math., 241(2001),
153-170).
