, Volume 172, Issue 1, pp 5160
First online:
The road coloring problem
 A. N. TrahtmanAffiliated withDepartment of Mathematics, BarIlan University Email author
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A 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 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 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 noticeable interest among the specialists in the theory of graphs, deterministic automata and symbolic dynamics. The positive solution of the road coloring problem is presented.
 Title
 The road coloring problem
 Journal

Israel Journal of Mathematics
Volume 172, Issue 1 , pp 5160
 Cover Date
 200907
 DOI
 10.1007/s1185600900625
 Print ISSN
 00212172
 Online ISSN
 15658511
 Publisher
 The Hebrew University Magnes Press
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 Authors

 A. N. Trahtman ^{(1)}
 Author Affiliations

 1. Department of Mathematics, BarIlan University, 52900, Ramat Gan, Israel