Factorization of de Bruijn digraphs by cycle-rooted trees

Abstract

In this paper, we introduce a new concept of an arc-coloring of digraphs called in-coloring. An in-coloring of an in-regular digraph induces a factorization into cycle-rooted trees; a cycle-rooted tree is a weakly connected digraph in which every vertex has indegree one. In particular, we study in-colorings of a line digraph. The results interpolate one-factorizations and tree factorizations of the de Bruijn digraph.