On potentially (K(,4) - e)-graphic sequences

An n-term nonincreasing nonnegative integer sequence π = (d₁, d₂ ,,d_n) is said to be graphic if it is the degree sequence of a simple graph G of order n, and such graph G is referred to as a realization of π. Let H be a simple graph. A graphic sequence π is said to be potentially H-graphic if it has a realization G containing H as a subgraph. In this paper, we characterize the potentially (K _k − e)-graphic sequences for k = 4, 5, where (K_k − e) is the graph obtained from K_k by removing one edge. This characterization implies a theorem due to C. H. Lai [15] and a characterization of potentially C₄-graphic sequences due to R. Luo [20].