De Bruijn Graph Homomorphisms and Recursive De Bruijn Sequences

2008/12/21 by Abbas Alhakim, Alhakim, Abbas, Mufutau Akinwande +1
Computer Science · Mathematics · #68R05 #68R10 #68R15 #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.IT #math.CO #math.IT #msc:68R05 #msc:68R10 #msc:68R15

paper · pdf · doi:10.48550/arxiv.0812.4012

15 pages, 1 figure, 2 tables, submitted

arxiv created 2008/12/21 · arxiv updated 2009/12/01

Abstract

This paper presents a method to find new De Bruijn cycles based on ones of lesser order. This is done by mapping a De Bruijn cycle to several vertex disjoint cycles in a De Bruijn digraph of higher order and connecting these cycles into one full cycle. We characterize homomorphisms between De Bruijn digraphs of different orders that allow this construction. These maps generalize the well-known D-morphism of Lempel between De Bruijn digraphs of consecutive orders. Also, an efficient recursive algorithm that yields an exponential number of nonbinary De Bruijn cycles is implemented.

Related

• Hamiltonicity of the Cross-Join Graph of de Bruijn Sequences
• Contributions to the theory of de Bruijn cycles
• Extending de Bruijn sequences to larger alphabets
• Binary de Bruijn Sequences via Zech's Logarithms
• Constructing de Bruijn sequences by concatenating smaller universal cycles