We study the Hamilton cycle problem with input a random graph G=G(n,p) in two settings. In the first one, G is given to us in the form of randomly ordered adjacency lists while in the second one we are given the adjacency matrix of G. In each of the settings we give a deterministic algorithm that w.h.p. either it finds a Hamilton cycle or it returns a certificate that such a cycle does not exists, for p > 0. The running times of our algorithms are w.h.p. O(n) and O(n/p) respectively each being best possible in its own setting.

翻译：我们用输入两个设置的随机图形 G=G(n,p) 来研究汉密尔顿周期问题。 在第一个设置中, G 以随机订购的相邻列表的形式提供给我们,而在第二个设置中, 我们得到 G 的相邻矩阵。 在每一个设置中, 我们给出一个确定性算法, 它要么找到一个汉密尔顿周期, 要么它返回一个不存在该周期的证书, p > 0。 我们算法的运行时间在自己的设置中是最好的。