Properly colored hamilton cycles in edge-colored complete graphs

It is shown that, for ϵ>0 and n>n₀(ϵ), any complete graph K on n vertices whose edges are colored so that no vertex is incident with more than (1-1/sqrt2-epsilon)n edges of the same color contains a Hamilton cycle in which adjacent edges have distinct colors. Moreover, for every k between 3 and n any such K contains a cycle of length k in which adjacent edges have distinct colors. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 , 179–186 (1997)