The smallest degree sum that yields potentially K r1,r2,...,rl,2,s-graphic sequences - Yin, Jian-Hua; Yin, Meng-Xiao (Utilitas Mathematica, 2009)
Let σ(Kr1,r2,...,re,r,s, n) be the smallest even integer such that every n-term graphic sequence π = (d1, d2 , dn) with term sum σ(π) = d1 + d2 + ... + dn ≥ σ(Kr1,r2,...,re,r,s, n) has a realization G containing Kr1,r2,...,re,r,s as a subgraph, where s≥r≥re≥...≥r1≥0 and Kr1,r2,...,re,r,s is the r1 × r2 × ... × re × r × s complete (l + 2)-partite graph. In this paper, we determine σ(Kr1,r2,...,re,2,s, n) for s ≥ 3 and n ≥ 2s2 + 8s + 3(r1 + r2 + .. + re) + 4.