Simplicial simple-homotopy of flag complexes in terms of graphs

Details Simplicial simple-homotopy of flag complexes in terms of graphs Simplicial simple-homotopy of flag complexes in terms of graphs

2008-09-10

arxiv.org/abs/0809.1751v2

Mathematics

Combinatorics

15 pages, 8 figures (in tex format; uses pstricks)

Scientific paper

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).

Affiliated with

Also associated with

No associations

Rating

Simplicial simple-homotopy of flag complexes in terms of graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Simplicial simple-homotopy of flag complexes in terms of graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Simplicial simple-homotopy of flag complexes in terms of graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-161311