  The synchronizing word of 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 is synchronizing if the
coloring turns the graph into deterministic finite automaton possessing a
synchronizing word.
  The road coloring problem is a problem of synchronizing coloring of directed
finite strongly connected graph with constant outdegree of all its vertices if
the greatest common divisor of lengths of all its cycles is one. The problem
was posed by Adler, Goodwyn and Weiss over 30 years ago and evoked a noticeable
interest among the specialists in theory of graphs, deterministic automata and
symbolic dynamics. The problem is described even in "Wikipedia" - the popular
Internet Encyclopedia. The positive solution of the road coloring problem is
presented.
