It was recently proved that every planar graph is a subgraph of the strongproduct path and with bounded treewidth. This paper surveys generalisationsof this result for graphs on surfaces, minor-closed classes, various nonminor-closed classes polynomial growth. We then explorehow product structure might be applicable to more broadly defined graphclasses. In particular, we characterise when class...

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...