A characterization for a sequence to be potentially Kr+1 - E(P2), K-2r+1-graphic - Wang, Ye; Yin, Jian-Hua (Utilitas Mathematica, 2012)
Let n ≥ r, πr = (d1, d2... ,dn) be a non-increasing sequence of nonnegative integers and Kr+1 -E(P 2) (resp. K-2r+1) be the graph obtained from Kr+1 by deleting two edges which are adjacent (resp. which are not adjacent). If π has a realization G containing Kr+1-E(P 2) (resp. K-2r+1) as a subgraph, then π is said to be potentially Kr+1-E(P2) (resp. K -2r+1)-graphic. In this paper, we give a characterization for a sequence π to be potentially Kr+1 - E(P2)-graphic and a characterization for a sequence π to be potentially K -2r+1-graphic.