On the Road Coloring Problem
نویسندگان
چکیده
منابع مشابه
The Road Coloring Problem
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 d...
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 کاملA Note on Synchronized Automata and Road Coloring Problem
We consider a problem of labeling a directed multigraph so that it becomes a synchronized finite automaton, as an ultimate goal to solve the famous Road Coloring Conjecture, cf. [1,2].We introduce a relabeling method which can be used for a large class of automata to improve their “degree of synchronization”. This allows, for example, to formulate the conjecture in several equivalent ways.
متن کاملA Note on the Road-Coloring Conjecture
Some results relating to the road-coloring conjecture of Alder, Goodwyn, and Weiss, which give rise to an O(n2) algorithm to determine whether or not a given edge-coloring of a graph is a road-coloring, are noted. Probabilistic analysis is then used to show that, if the outdegree of every edge in an n-vertex digraph is δ = ω(logn), a road-coloring for the graph exists. An equivalent re-statemen...
متن کاملOn the General Coloring Problem
Generalizing relational structures and formal languages to structures whose relations are evaluated by elements of a lattice, we show that such structure classes form a Heyting algebra if and only if the evaluation lattice is a Heyting algebra. Hence various new and some older results obtained for Heyting algebras can be applied to such structure classes.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1990
ISSN: 0002-9939
DOI: 10.2307/2047767