On extremal factors of de Bruijn-like graphs

08/30/2023

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by   Nicolás Álvarez, et al.

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In 1972 Mykkeltveit proved that the maximum number of vertex-disjoint cycles in the de Bruijn graphs of order n is attained by the pure cycling register rule, as conjectured by Golomb. We generalize this result to the tensor product of the de Bruijn graph of order n and a simple cycle of size k, when n divides k or vice versa. We also develop counting formulae for a large family of cycling register rules, including the linear register rules proposed by Golomb.