English

On extremal factors of de Bruijn-like graphs

Combinatorics 2024-07-29 v1 Discrete Mathematics

Abstract

In 1972 Mykkeltveit proved that the maximum number of vertex-disjoint cycles in the de Bruijn graphs of order nn 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 nn and a simple cycle of size kk, when nn divides kk or vice versa. We also develop counting formulae for a large family of cycling register rules, including the linear register rules proposed by Golomb.

Keywords

Cite

@article{arxiv.2308.16257,
  title  = {On extremal factors of de Bruijn-like graphs},
  author = {Nicolás Álvarez and Verónica Becher and Martín Mereb and Ivo Pajor and Carlos Miguel Soto},
  journal= {arXiv preprint arXiv:2308.16257},
  year   = {2024}
}