198k views
3 votes
If G contains a trail from x to y, then G contains a path from x to y.

a) True

b) False

1 Answer

2 votes

The given statement "If G contains a trail from x to y, then G contains a path from x to y" is true.

The statement is true because a trail is a sequence of edges in a graph where no edge (or vertex) is repeated. If a graph G contains a trail from vertex x to vertex y, it implies that there exists a sequence of edges that connects x to y without revisiting any edge. Since a path is a more general concept that allows for repeated vertices but not repeated edges, any trail can be considered a path.

Therefore, if G contains a trail from x to y, it also contains a path from x to y. In graph theory, a trail is a specific type of path, and the presence of a trail ensures the existence of a more general path between the specified vertices in the graph. Hence the given statement is true.

User Gor
by
7.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.