Prove Lemma 10.1.1(a): If G is a connected graph, then any two distinct vertices of G can be connected by a path. (You may use the result stated in exercise 43.)
If G is a connected graph, then any two distinct vertices of G can be connected by a path.
G is a connected graph.
Let G be a connected graph and let u and v be two distinct vertices of G.
Since G is connected, there exists a walk W between u and v.
If W contains a repeated vertex v, then delete the part of the walk between the two occurrences of v and rename the resulting walk as W...
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