On the Hybrid Cerný-Road Coloring Problem and Hamiltonian Paths

The Hybrid Cerny-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.

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