Connectedness of the Degree Bounded Star Process

In this paper we consider a random star d-process which begins with n isolated vertices and in each step chooses randomly a vertex of current minimum degree #, and connects it with d # random vertices of degree less than d. We show that 3 the resulting final graph is connected with probability 1 o(1), and moreover that for su#ciently large d it is d-connected with probability 1 o(1)

Language Reference

Connectedness of the degree bounded star process. (English summary) Combinatorics, probability and computing (Oberwolfach, 2001). Combin. Probab. Comput. 12 (2003), no. 3, 269–283. Summary: “In this paper we consider a random star d-process which begins with n isolated vertices and in each step chooses randomly a vertex of current minimum degree δ, and connects it with d − δ random vertices of degree less than d. We show that, for d ≥ 3, the resulting final graph is connected with probability 1 − o(1), and moreover that, for sufficiently large d, it is d-connected with probability 1 − o(1).” Reviewed by Dudley Star