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arXiv · 2308.16257

On extremal factors of de Bruijn-like graphs

Nicolás Álvarez·Verónica Becher·Martín Mereb·Ivo Pajor·Carlos Miguel Soto
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Abstract

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.

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Nicolás Álvarez, Verónica Becher, Martín Mereb, Ivo Pajor, Carlos Miguel Soto. 2023-08-30. On extremal factors of de Bruijn-like graphs. https://doi.org/10.1016/j.dam.2024.06.010

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