The enumerative theory of simplicial subdivisions (triangulations) of simplicial complexes was developed by Stanley in order to understand the effect of such subdivisions on the h-vector of a simplicial complex. A key role there is played by the concept of a local h-vector. This paper surveys some of the highlights of this theory and recent developments, concerning subdivisions of flag homology...

In this paper, we apply the Turan sieve and simple developed by R. Murty first author to study problems in random graph theory. particular, obtain upper lower bounds on probability of a n vertices having diameter 2 (or 3 case bipartite graphs) with edge p(n) where edges are chosen independently . An interesting feature revealed these results is that `almost completely' complement each other. As...