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If G contains a trail from x to y, then G contains a path from x to y.
- True
- False

User Glr
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1 Answer

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Final answer:

The statement that if a graph contains a trail from x to y, then it contains a path from x to y is true, because a path is a trail without repeated vertices and can be obtained by removing loops from the trail.

Step-by-step explanation:

The statement is true. If graph G contains a trail from vertex x to vertex y, this means that we can traverse from x to y by following edges, where each edge is used only once. However, a trail can include revisiting vertices. A path, on the other hand, is a sequence of edges connecting two vertices without traversing any vertex more than once.

To transform a trail into a path, one simply needs to eliminate any loops or repeated visits to vertices within the trail. Hence, every trail from x to y contains at least one path from x to y. By following the trail and omitting any circular routes or repeated sections, you can form a path.

User FloatingKiwi
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