A KINETIC APPROACH TO THE RANDOM F-GRAPH PROCESS - PATHS, CYCLES AND COMPONENTS

Starting with n labeled vertices and no edges, introduce edges, one at a time, so as to obtain a sequence of graphs each having no vertex of degree greater than f. The latter are called f-graphs. At each step t he edge to be added is selected with equal probability from among thos e edges whose addition would not violate the f-degree restriction. Thi s procedure is called the Random f-graph Process (Rf-GP) of older n. H ere we determine some properties of the numbers of paths, cycles and c omponents for the R2-GP and provide the vertex degree distribution for all f greater than or equal to 2.