The sequential generation of random \(f\)-graphs. Distributions and predominant types of edge maximal \(f\)-graphs with \(f>4\) (Q685646)

An \(f\)-graph is a graph whose vertices are all of degree no greater than \(f\); an edge-maximal \(f\)-graph is an \(f\)-graph such that adding any edges will make one of the vertices of degree \(f+1\). One can generate random edge-maximal \(f\)-graphs by adding edges randomly, one at a time, until it is an edge-maximal \(f\)-graph. This note lists some of the facts known and problems for the probabilities \(P(m;n;f)=\) the probability that such a randomly generated edge-maximal \(f\)-graph on \(n\) vertices has \(m\) vertices of degree \(<f\).