变振铃与哈密顿圈：Erin和Stedman三元组的寻找
Change Ringing and Hamiltonian Cycles : The Search for Erin and Stedman Triples
摘要：
在钟学中一个非常古老的问题是寻找珍珠。后者可以被认为是给定大小的所有可能排列的严格约束序列，其中约束的确切性质取决于期望的振铃方法。特别是，我们考虑的方法，只有bobs-Stedman三元组和Erin三元组，后者的存在性仍然是一个悬而未决的问题。我们表明，这个问题可以被看作是一个类似的约束形式的哈密顿圈问题（HCP）。通过使用特殊子图，我们将其转换为HCP的标准实例。原来的问题可以划分成更小的实例，所以我们使用这种技术来产生更小的HCP的实例。我们注意到，已知有解的实例提供了HCP的异常困难的实例。
英文摘要：
A very old problem in campanology is the search for peals. The latter can be thought of as a heavily constrained sequence of all possible permutations of a given size, where the exact nature of the constraints depends on which method of ringing is desired. In particular, we consider the methods of bobs-only Stedman Triples and Erin Triples; the existence of the latter is still an open problem. We show that this problem can be viewed as a similarly constrained form of the Hamiltonian cycle problem (HCP). Through the use of special subgraphs, we convert this to a standard instance of HCP. The original problem can be partitioned into smaller instances, and so we use this technique to produce smaller instances of HCP as well. We note that the instances known to have solutions provide exceptionally difficult instances of HCP.
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