On extremal factors of the de Bruijn graph

Abstract

An outstanding problem in combinatorial theory is to determine the maximum number of vertex-disjoint cycles in the n-th order de Bruijn graph G n . A related problem is to determine the minimum number of vertices which, if removed from G n , will leave a graph with no cycles. Both problems are discussed and it is shown that for n ≤ 8 the same number is attained for both. Further results indicate that the same is likely to be true for all values of n.