A property of the colored complete graph

If the lines of the complete graph K_n are colored so that no point is on more than $\text{1}\text{7}\text{(n?1)}$ lines of the same color or so that each point lies on more than $\text{1}\text{7}\text{(5n+8)}$ lines of different colors, then K_n contains a cycle of length n with adjacent lines having different colors.