On potentially Kr1,r2...rm -graphic sequences - Yin, Jian-Hua; Chen, Gang (Utilitas Mathematica, 2007)
For given a graph II, a graphic sequence π = (d1, d 2,..., dn) is said to be potentially H-graphic if there exists a realization of π containing H as a subgraph. In this paper, we determine the smallest even integer σ(K1s, t, n) such that each n-term graphic sequence with term sum at least σ(K1s, t, n) is potentially K1s, t-graphic, where n ≥ 3s + 2t2+ 3t - 3 and K1s, t is an r1 × r2 × ⋯ × rs+1 complete a s + 1-partite graph with r 1 = r2 = ⋯ = rs, = 1 and rs+1 = t. Moreover, we also characterize the potentially Kr, s-graphic sequences without zero terms for r = 2, s = 3 and r = 2, s = 4, where K r,s is an r × s complete bipartite graph.