On the hybrid Černý-road coloring problem and Hamiltonian paths

Authors:
Arturo Carpi;Flavio D'Alessandro
Affiliations:
Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy;Dipartimento di Matematica, Università di Roma "La Sapienza", Roma, Italy and Department of Mathematics, Boğaziçi University, Istanbul, Turkey
Venue:
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Year:
2010

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Abstract

The Hybrid Černy-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.