  Quasi-Sturmian words, which are infinite words with factor complexity
eventually $n+c$ share many properties with Sturmian words. In this paper, we
study the quasi-Sturmian colorings on regular trees. There are two different
types, bounded and unbounded, of quasi-Sturmian colorings. We obtain an
induction algorithm similar to Sturmian colorings. We distinguish them by the
recurrence function.
