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A Characterization of Maximum Independent Sets of de Bruijn Graphs

The de Bruijn graph B(d, 3) consists of all strings of length 3, taken from an alphabet of size d, with edges between words which are distinct substrings of a word of length 4. We give an inductive characterization of the maximum independent sets of the de Bruijn graphs B(d, 3) and for the de Bruijn graph with loops removed, for all d. We derive a recurrence relation for their number.