The generalized road coloring problem and periodic digraphs
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...
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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...
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The dichromatic number ~ χ(D) of a digraph D is the least number k such that the vertex set of D can be partitioned into k parts each of which induces an acyclic subdigraph. Introduced by Neumann-Lara in 1982, this digraph invariant shares many properties with the usual chromatic number of graphs and can be seen as the natural analog of the graph chromatic number. In this paper, we study the li...
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We consider vertex coloring of an acyclic digraph ~ G in such a way that two vertices which have a common ancestor in ~ G receive distinct colors. Such colorings arise in a natural way when bounding space for various genetic data for efficient analysis. We discuss the corresponding chromatic number and derive an upper bound as a function of the maximum number of descendants of a given vertex an...
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.
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ژورنال
عنوان ژورنال: Applicable Algebra in Engineering, Communication and Computing
سال: 2010
ISSN: 0938-1279,1432-0622
DOI: 10.1007/s00200-010-0135-z