A characterization for a sequence to be potentially {Kr+1 - E(P2), Kr+1-2}-graphic

Let n >= r, pi = (d(1) ,d(2), ... , d(n)) be a non-increasing sequence of nonnegative integers and Kr+1 - E(P-2) (resp. K-r+1(-2)) be the graph obtained from Kr+1 by deleting two edges which are adjacent (resp. which are not adjacent). If it has a realization G containing Kr+1 - E(P-2) (resp. K-r+1(-2)) as a subgraph, then it is said to be potentially Kr+1 - E(P-2) (resp. K-r+1(-2))-graphic. In this paper, we give a characterization for a sequence pi to be potentially Kr+1 - E(P-2)-graphic and a characterization for a sequence pi to be potentially K-r+1(-2)-graphic.