The Road Coloring Problem
نویسنده
چکیده
The road coloring problem is an interesing problem proposed over 40 years ago by Adler, Goodwyn and Weiss. Hundreds of mathematicians worked on this problem and failed to make the conjecture a theorem. Finally, in 2007, it was proved by a 60-year-old Israeli mathematician, Avraham Trahtman. It turns out the prove was quite simple after Trahtman partitioned the graph into cycles and trees. The details are stated below.
منابع مشابه
Synchronizing Road Coloring
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 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...
متن کاملThe Visualization of the Road Coloring Algorithm in the package TESTAS
A problem of a visual image of a directed finite graph has appeared in the study of the road coloring conjecture. Given a finite directed graph, a coloring of its edges turns the graph into finite-state automaton. The visual perception of the structure properties of automata is an important goal. A synchronizing word of a deterministic automaton is a word in the alphabet of colors of its edges ...
متن کاملA Subquadratic Algorithm for Road Coloring
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 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...
متن کاملThe Road Coloring for Mapping on k States
Let Γ be directed strongly connected finite graph of uniform outdegree (constant outdegree of any vertex) and let some coloring of edges of Γ turn the graph into deterministic complete automaton. Let the word s be a word in the alphabet of colors (considered also as letters) on the edges of Γ and let Γs be a mapping of vertices Γ. A coloring is called k-synchronizing if for any word t |Γt| ≥ k ...
متن کاملThe road coloring problem
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 direc...
متن کامل