On potentially P-graphic degree sequences

A sequence 1l = (d 1 ,d 2 , ... ,d n) of positive integers is said to be graphic if there exists a simple graph G such that 1£ is the degree sequence of G. For a specified property P of graphs. a sequence 1l = (d 1 ,d 2 • ... • d n) of positive integers is said to be potentially P-graphic if 1l is graphic and there exists a realization of 1l with the property P. In this paper we characterize potentially P-graphic sequences where P is one of the following properties (i) connected and each block is a clique on k vertices. (ii) connected and each block is a clique on kl\ or k2 vert~ces.