Lower Bounds of a Feedback Function

The Upper Bounds of a Feedback Function

“…Now we are recalling some basic notions from [8]. [ip] is said to be the factor of the de Bruijn graph B k of order k corresponding to ip, as it is a maximal subgraph of B k consisting of the circuits, (cf.…”

“…As it has been stated in [8], the family of lower bounds of a feedback function -which forms an upper semilattice -is described by a binary relation, called the independent splits relation, closely related to the interlacing relation defined in [6].…”

Colouring of cycles in the de bruijn graphs

“…Therefore it is necessary to see connections between the factors. In the paper [7] a certain order in the family of the factors of the de Bruijn graph was studied. Here the factors forming the Hamiltonian cycles are the maximal elements and locally reducible factors defined in [11] are the minimal elements.…”

“…On the other hand, in the de Bruijn graph of order k the cycles of the locally reducible factors are determined by the cycles of the de Bruijn graph of order k − 1 in such a way that a sequence of succeding vertices of each cycle in the locally reducible factor is a sequence of succeding edges in a certain cycle of the de Bruijn graph of order k − 1. The construction of all locally reducible factors in the de Bruijn graph of order k and next of all maximal chains (according to the order considered in [7]) containing a certain factor forming the Hamiltonian cycle in this graph allow to give a detailed description of its structure. It is very important for the mentioned problem of the construction and the analysis of the cryptographic systems [8].…”