  A word $\bar{w} = \bar{u}\bar{u}$ is a $long$ $square$ if $\bar{u}$ is of
length at least 3; a word $\bar{w}$ is $long$-$square$-$free$ if $\bar{w}$
contains no sub-word that is a long square. We can use words to generate graph
colorings; a graph coloring is called $long$-$repetition$-$free$ if the word
formed by the coloring of each path in the graph is long-square-free. Our
results show that every rooted tree of radius less than or equal to seven is
long-repetition-free two-colorable. We also prove there exists a class of trees
which are not long-repetition-free two-colorable.
