On potentially Κ;2,2,1,1-graph 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 exists a realization of π containing H as a subgraph. In this paper, we characterize the potentially Κ;_2,2,1,1-graph sequences where Κ;_r,s,p,t is an rxsxpxt complete 4-partite graph. Up to now, characterization of potentially complete 4-partite graph with κ;(κ; ≤ 6) vertices has solved.