An Extremal Problem On Potentially K_r,s,t-Graphic Sequences

A variation of classical Turan-type extremal problems is considered as follows: for a given graph H, determine the smallest even interger σ(H,n) such that every n-term positive graphic sequence Ï€= (d₁,d₂,... ,d_m) with term sum σ (Ï€)= d₁+d₂ + .... + d_n≥ σ(H,n) has a realization G containing H as a subgraph. For H = K_k+1, Erdos, Jacobson and Lehel conjectured that σ(K_k+1,n) = (k + l)(2n - k) + 2 for sufficiently large n. Recently Li et al. proved that conjecture is true. In recent, Yin et al. further determined the values of σ(K_r,s n). This thesis mainly considers the problem of determing the values of σ(K_r,s,t n), and obtain the following results:1.Determining the values of σ(K_1,2,3 , n) for n ≥ 6;2.Determining the values of σ(K_{1,2,s n} for s ≥ 4 and n ≥ 2[(s+4)² /4 ] + 8.