We consider a Hamiltonian decomposition problem of partitioning a regular graph into edge-disjoint Hamiltonian cycles. A sufficient condition for vertex adjacency in the 1-skeleton of the traveling salesperson polytope can be formulated as the Hamiltonian decomposition problem in a 4-regular multigraph. We introduce a heuristic general variable neighborhood search algorithm for this problem based on finding a vertex-disjoint cycle cover of the multigraph through reduction to perfect matching and several cycle merging operations. The algorithm has a one-sided error: the answer “not adjacent” is always correct, and was tested on random directed and undirected Hamiltonian cycles and on pyramidal tours.

我们考虑将规则图划分为边不相交的哈密顿循环的哈密顿分解问题。可以将旅行营业员多面体的1骨架中顶点邻接的充分条件公式化为4正则多图中的汉密尔顿分解问题。我们针对此问题引入启发式一般变量邻域搜索算法，该算法基于通过简化至完全匹配和多次循环合并操作找到多图的顶点不相交的循环覆盖。该算法有一个单方面的错误：答案“不相邻”始终是正确的，并在随机的有向和无向哈密顿循环以及金字塔巡回测试中进行了测试。