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Published in:
2010 | OriginalPaper | Chapter
On the Hybrid Černý-Road Coloring Problem and Hamiltonian Paths
Authors : Arturo Carpi, Flavio D’Alessandro
Published in: Developments in Language Theory
Publisher: Springer Berlin Heidelberg
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The Hybrid Černý-Road coloring problem is investigated for graphs with Hamiltonian paths. We prove that if an aperiodic, strongly connected digraph of costant outdegree with
n
vertices has an Hamiltonian path, then it admits a synchronizing coloring with a reset word of length 2(
n
− 2)(
n
− 1) + 1. The proof is based upon some new results concerning locally strongly transitive automata.