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.

翻译：1972年，Mykkeltveit证明了Golomb提出的猜想：在$n$阶de Bruijn图中，顶点不交环的最大数目可通过纯循环寄存器规则实现。本文将这一结果推广至$n$阶de Bruijn图与大小为$k$的简单环的张量积情形，其中$n$整除$k$或$k$整除$n$。此外，我们为一大类循环寄存器规则（包括Golomb提出的线性寄存器规则）建立了计数公式。