On the characterization of potentially Κ1,1,s-graphic sequences

Abstract

For given a graph H, a graphic sequence π = (d₁, d ₂,⋯, d_n) 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 Κ_1,1,s-positive graphic sequences for s = 4 and 5, where Κ_1,1,s is the 1 x 1 x s complete 3-partite graph. These characterizations imply the values of σ (Κ_1,1,s,n) for s = 4 and 5.