On potentially Kr+1 - U-graphical sequences - Lai, Chunhui,; Yan, Guiying, (Utilitas Mathematica, 2009)
Let Km - H be the graph obtained from Km by removing the edges set E(H) of the graph H (H is a subgraph of Km). We use the symbol Z4 to denote K4 - P2. A sequence S is potentially Km - H-graphical if it has a realization containing a Km-H as a subgraph. Let σ(Km-H, n) denote the smallest degree sum such that every n-term graphical sequence S with σ(S) ≥ σ(Km - H,n) is potentially Km - H-graphical. In this paper, we determine the values of σ(Kr+1 - U, n) for n ≥ 5r +18, r +1 ≥ k ≥ 7,j≥6 where U is a graph on A; vertices and j edges which contains a graph K3 ∪ P3 but not contains a cycle on 4 vertices and not contains Z4.