Given a
graph
*G*, we define a *path* between two vertices
*v* and *w* of *G* to be a sequence of edges
*e*_{1},
*e*_{2},...,
*e*_{n}
such that *v* is an endpoint of *e*_{1},
*w* is an endpoint of *e*_{n}, and for each
*i*=1...n-1, edges *e*_{i} and *e*_{i+1} share
a common endpoint.

In this graph, there is a path
between vertices *a* and *f*. There is no path
between vertices *a* and *k*

*Back to the Parallel Mountain Climbers problem**
*