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arXiv · 2607.12078

Completely Reachable Road Coloring

Mikhail V. Volkov·Yinfeng Zhu
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Abstract

We characterize the digraphs that admit an edge labeling by letters from a finite alphabet such that the resulting labeled digraph is a completely reachable automaton. This class of digraphs can be recognized in polynomial time. In contrast, we show that, for every fixed alphabet size, the problem of deciding whether a digraph admits an edge labeling with the same property is NP-complete. We also classify the digraphs for which every edge labeling results in a completely reachable automaton.

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Mikhail V. Volkov, Yinfeng Zhu. 2026-08-31. Completely Reachable Road Coloring. https://arxiv.org/abs/2607.12078

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