# Tour vs Path in graph theroy

English is not my mother tongue so I don´t know exactly wich is the difference between a tour and path in graphs theory context. I think that in both cases it is a way throught various vertex or points. Is this correct?

• Usually, a path connects two vertices without repeat. A tour goes though all vertices. Aug 22, 2017 at 14:53
• So the difference is if vertices are repeated?
– Ixer
Aug 22, 2017 at 15:10
• All vertices -- tour. Some vertices -- path. Neither repeats a vertex. Aug 22, 2017 at 15:11
• Seems that a tour is a clycle according to this phrase in wikipedia :"A Hamiltonian cycle, Hamiltonian circuit, vertex tour or graph cycle is a cycle that visits each vertex exactly once (except for the vertex that is both the start and end, which is visited twice)." Is this incorrect in wikipedia?
– Ixer
Aug 22, 2017 at 15:40

Walk - A sequence of vertices and edges, where the edges connect the adjacent vertices in the sequence

Tour - a walk with no repeated edges

Path - a walk with no repeated vertices

Source: CS 70 MT1 Review Spring 2018 @ UC Berkeley

• can you link to the cs70 review? Sep 7, 2020 at 22:55

A path is a walk with no repeated vertices.

A trail is a walk with no repeated edges.

A tour is a walk that visits every vertex returning to its starting vertex. A tour could visit some vertices more than once. If you visit them exactly once, then the tour is a Hamiltonian cycle.

A cycle is a walk in which the end vertex is the same as the start vertex and no other vertex is visited more than once.