IWOCA 2011: Combinatorial Algorithms pp 324-336

# Hamilton Cycles in Restricted Rotator Graphs

• Brett Stevens
• Aaron Williams
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7056)

## Abstract

The rotator graph has vertices labeled by the permutations of n in one line notation, and there is an arc from u to v if a prefix of u’s label can be rotated to obtain v’s label. In other words, it is the directed Cayley graph whose generators are $$\sigma_{k} := (1 \ 2 \ \cdots \ k)$$ for 2 ≤ k ≤ n and these rotations are applied to the indices of a permutation. In a restricted rotator graph the allowable rotations are restricted from k ∈ {2,3,…,n} to k ∈ G for some smaller (finite) set G ⊆ {2,3,…,n}. We construct Hamilton cycles for G = {n−1,n} and G = {2,3,n}, and provide efficient iterative algorithms for generating them. Our results start with a Hamilton cycle in the rotator graph due to Corbett (IEEE Transactions on Parallel and Distributed Systems 3 (1992) 622–626) and are constructed entirely from two sequence operations we name ‘reusing’ and ‘recycling’.

## Keywords

Cayley Graph Hamilton Cycle Gray Code Successor Rule Hamilton Sequence
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Brett Stevens
• 1
• Aaron Williams
• 1