能否有人告诉我哈密尔顿路径和欧拉路径之间的差异。他们似乎相似！

Can some one tell me the difference between hamiltonian path and euler path. They seem similar!

推荐答案

一个欧拉路径是穿越每条边恰好一次不重复，如果它在初始顶点结束那么它是一个欧拉循环的路径。

A Euler path is a path that crosses every edge exactly once without repeating, if it ends at the initial vertex then it is a Euler cycle.

一个哈密尔顿路径，通过每一个顶点（注意不是每边）传递，只有一次，如果它在初始顶点结束那么它是一个汉密尔顿的周期。

A Hamiltonian path passes through each vertex (note not each edge), exactly once, if it ends at the initial vertex then it is a Hamiltonian cycle.

在一个欧拉路径，你可以通过一个顶点超过一次。

In a Euler path you might pass through a vertex more than once.

在一个哈密尔顿路径，你可能无法通过，虽然所有的边缘。

In a Hamiltonian path you may not pass though all edges.