Elsevier

Discrete Mathematics

Volume 309, Issue 17, 6 September 2009, Pages 5298-5304
Discrete Mathematics

Minimum Eulerian circuits and minimum de Bruijn sequences

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Abstract

Given a digraph (directed graph) with a labeling on its arcs, we study the problem of finding the Eulerian circuit of lexicographically minimum label. We prove that this problem is NP-complete in general, but if the labelling is locally injective (arcs going out from each vertex have different labels), we prove that it is solvable in linear time by giving an algorithm that constructs this circuit. When this algorithm is applied to a de Bruijn graph, it obtains the de Bruijn sequences with lexicographically minimum label.

Keywords

Eulerian circuits
Labelled digraph
De Bruijn sequences

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This work was partially supported by Proyecto Anillo en Redes and Fondecyt 1060825.