On the distribution in a graph process
A graph \(G_{n+1}\) is obtained from a graph \(G_ n\) by adding a new point with probability \(p_ n\) and inserting a new line at random with probability \(1-p_ n\) for \(n=1,2,...\). Here \(p_ n=1\) if \(G_ n\) is complete, and \(p_ n=p\) otherwise. The initial graph \(G_ 1\) consists of a simple point. Various properties of the graph process were investigated by \textit{M. Capobianco} and \textit{O. Frank} [Discrete Math. 46, 133-143 (1983; Zbl 0513.05049)] using lattice path methods. This note shows how determinantal lattice path counting formulas can be applied in this context.
scientific article; zbMATH DE number 3863237