The Generalized Road Coloring Problem and periodic digraphs
Greg Budzban, Philip Feinsilver
TL;DR
This paper proves the Generalized Road Coloring Problem using algebraic and algorithmic methods, studying periodic digraphs and Markov chains to establish new characterizations and solutions.
Contribution
It provides an independent proof of the problem and introduces algebraic conditions for periodic, strongly connected digraphs.
Findings
Proof of the Generalized Road Coloring Problem independent of recent work
Algebraic characterization of periodic, strongly connected digraphs
Application of semigroup methods and Trakhtman's algorithm
Abstract
A proof of the Generalized Road Coloring Problem, independent of the recent work by Beal and Perrin, is presented, using both semigroup methods and Trakhtman's algorithm. Algebraic properties of periodic, strongly connected digraphs are studied in the semigroup context. An algebraic condition which characterizes periodic, strongly connected digraphs is determined in the context of periodic Markov chains.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Advanced Combinatorial Mathematics