Which of the following statements about trails is true?

The statement that a trail cannot revisit vertices is accurate within the context of graph theory. In graph theory, a trail is a walk in which no edges are repeated, though vertices may be revisited. Therefore, while it is true that a trail cannot traverse the same edge multiple times, it is permitted to visit the same vertex multiple times.

In contrast, the claim that a trail must start and end at the same vertex is incorrect, as trails can begin and end at different vertices. This mischaracterization defines a closed trail or circuit but does not apply to all trails.

Furthermore, the assertion that a trail can only exist in directed graphs is misleading. Trails can be found in both directed and undirected graphs, making this statement too restrictive.

Finally, the notion that a trail must cover all edges once is incorrect, as trails can include a selection of edges and do not need to encompass all available edges in the graph.

Hence, it is essential to understand that the conditions defining trails allow for the possibility of vertex revisits, which is not accurately represented in the statement provided.