On regular configurations and disjoint cycles in shift graphs

Details On regular configurations and disjoint cycles in shift graphs On regular configurations and disjoint cycles in shift graphs

2007-09-30

arxiv.org/abs/0710.0125v1

Mathematics

Combinatorics

25 pages, 8 figures, submitted

Scientific paper

Configurations are necklaces with prescribed numbers of red and black beads. Among all possible configurations, the regular one plays an important role in many applications. In this paper, several aspects of regular configurations are discussed, including construction, uniqueness, symmetry group and the link with balanced words. Another model of configurations is the polygons formed by a given number of sides of two different lengths. In this context, regular configurations are used to obtain a lower bound for the cycles packing number of shift graphs, a subclass of the directed circulant graphs.

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