A Rao-type characterization for a sequence to have a realization containing a split graph

For a given graph H , a non-increasing sequence π = ( d 1 , d 2 , … , d n ) of nonnegative integers is said to be potentially H -graphic if there exists a realization of π containing H as a subgraph. The split graph K r + K s ¯ on r + s vertices is denoted by S r , s . In this paper, we give a Rao-type characterization for π to be potentially S r , s -graphic. A simplification of this characterization is also presented.