论文标题
转向矩形网格的汉密尔顿周期
Turns in Hamilton cycles of rectangular grids
论文作者
论文摘要
对于在矩形$ m \ times n $网格中的汉密尔顿周期，可能发生的最大弯道是多少？在几种情况下，我们给出确切的答案，并在其他所有情况下回答$ 2 $的添加误差。特别是，我们为Beluhov的结果提供了新的证明，以$ n \ times n $网格的案例。我们的主要方法是“最大的转弯数”与“最小数量”的问题之间的令人惊讶的联系。
For a Hamilton cycle in a rectangular $m \times n$ grid, what is the greatest number of turns that can occur? We give the exact answer in several cases and an answer up to an additive error of $2$ in all other cases. In particular, we give a new proof of the result of Beluhov for the case of a square $n \times n$ grid. Our main method is a surprising link between the problem of 'greatest number of turns' and the problem of 'least number of turns'.
