On the five-color K_4 problem of the n -order complete graph

Let Kn be a complete graph with n vertices f(n) the smallest positive integer satisfying the following condition:for any positive integer m≥f(n) , there is an m -edge coloring of the Kn such that every K4 inKn gets at least 5 colors . Erdos andGyarfas gave the upper-lower bound of f(n):2/3n f(n)n and proved f(9)=8. In [3] Tang proved f(10)=9 and im-proved the lower bound of f( n):f( n)2/3n + 1 . In this paper , we prove f(11)=10 and improve the lower bound of f(n)further:f(n)1/8(6n-5) (n≥20) .