\magnification=1200 \hsize=4in \overfullrule=0pt \input amssym %\def\frac#1 #2 {{#1\over #2}} \def\emph#1{{\it #1}} \def\em{\it} \nopagenumbers \noindent % % {\bf Alan Frieze and Michael Krivelevich} % % \medskip \noindent % % {\bf On Rainbow Trees and Cycles} % % \vskip 5mm \noindent % % % % We derive sufficient conditions for the existence of rainbow cycles of all lengths in edge colourings of complete graphs. We also consider rainbow colorings of a certain class of trees. \bye .