论文标题
高度对称的汉密尔顿分解超管
A Highly Symmetric Hamilton Decomposition for Hypercubes
论文作者
论文摘要
图形的汉密尔顿分解是将其边缘设置为跨越循环的边缘的分配。这种分解的存在以均匀尺寸$ 2N $的所有超振管而闻名。我们给出了$ n = 2^a3^b $的情况的分解，这是高度对称的，从某种意义上说，每个周期都可以通过置换轴来从其他每个周期中得出。我们猜想每个n都存在类似的分解。
A Hamilton decomposition of a graph is a partitioning of its edge set into disjoint spanning cycles. The existence of such decompositions is known for all hypercubes of even dimension $2n$. We give a decomposition for the case $n = 2^a3^b$ that is highly symmetric in the sense that every cycle can be derived from every other cycle just by permuting the axes. We conjecture that a similar decomposition exists for every n.
