  A coloring of edges of a finite directed graph turns the graph into
finite-state automaton. The synchronizing word of a deterministic automaton is
a word in the alphabet of colors (considered as letters) of its edges that maps
the automaton to a single state. A coloring of edges of a directed graph of
uniform outdegree (constant outdegree of any vertex) is synchronizing if the
coloring turns the graph into a deterministic finite automaton possessing a
synchronizing word. The road coloring problem is the problem of synchronizing
coloring of a directed finite strongly connected graph of uniform outdegree if
the greatest common divisor of the lengths of all its cycles is one. The
problem posed in 1970 had evoked a noticeable interest among the specialists in
the theory of graphs, automata, codes, symbolic dynamics as well as among the
wide mathematical community. A polynomial time algorithm of $O(n^3)$ complexity
in the most worst case and quadratic in majority of studied cases for the road
coloring of the considered graph is presented below. The work is based on
recent positive solution of the road coloring problem. The algorithm was
implemented in the package TESTAS
