The road coloring and Černy conjecture

Avraham N. Trahtman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations


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. Some consequences on the length of the synchronizing word are discussed.

Original languageEnglish
Title of host publicationProceedings of the Prague Stringology Conference 2008
Number of pages12
StatePublished - 2008
EventPrague Stringology Conference 2008, PSC 2008 - Prague, Czech Republic
Duration: 1 Sep 20083 Sep 2008

Publication series

NameProceedings of the Prague Stringology Conference 2008


ConferencePrague Stringology Conference 2008, PSC 2008
Country/TerritoryCzech Republic


  • Deterministic finite automaton
  • Graph
  • Road coloring problem
  • Synchronization


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