Skip to main content
Article thumbnail
Location of Repository

Generalized de Bruijn Cycles

By Joshua N. Cooper and Ronald L. Graham


For a set of integers I, we define a q-ary I-cycle to be an assignment of the symbols 1 through q to the integers modulo q n so that every word appears on some translate of I. This definition generalizes that of de Bruijn cycles, and opens up a multitude of questions. We address the existence of such cycles, discuss “reduced ” cycles (ones in which the all-zeroes string need not appear), and provide general bounds on the shortest sequence which contains all words on some translate of I. We also prove a variant on recent results concerning decompositions of complete graphs into cycles and employ it to resolve the case of |I | = 2 completely

Topics: de Bruijn cycle, graph decomposition, probabilistic method
Year: 2004
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.