Tur(?)n's Problem And Ramsey Numbers For Trees With Order N And Maximal Degree N-4

For n>6,letand T_n⁴ =?V,E4?.In this paper,for p>n>10 we obtain explicit formulas for ex?p;T_n⁴?,where ex?p;L?denotes the maximal number of edges in a graph of order p not containing L as a subgraph.Suppose p = k?n-1?+ r,? ? ?1,2,3,...} and r ? {0,1,...,n-2}.If r ? ?3,4,...,n-8},thenwhere b is the least nonnegative residue of n-4 modulo r + 3 and[x]is the greatest integer not exceeding x.For r = n-7 we have ex{p;T_n⁴)=?n-2?p-4(n-4/2.Let r?G₁,G₂?be the Ramsey number of the two graphs G₁ and G₂.In this paper we also obtain some explicit formulas for r?Gm,T_n⁴?,where Gm is connected with order m ? n.In particular,if n>m + 2 ? 15,then...