On potentially H-graphic sequences

For given a graph H, a graphic sequence π = (d1, d2,..., dn) is said to be potentially H-graphic if there is a realization of π containing H as a subgraph. In this paper, we characterize the potentially (K5 − e)-positive graphic sequences and give two simple necessary and sufficient conditions for a positive graphic sequence π to be potentially K5-graphic, where Kr is a complete graph on r vertices and Kr-e is a graph obtained from Kr by deleting one edge. Moreover, we also give a simple necessary and sufficient condition for a positive graphic sequence π to be potentially K6-graphic.