Note: if you cannot remember the features of walks, trails and circuits, revise notes for 2.1 Introduction to Walks.
- A Eulerian trail is a trail which encompasses every edge of a graph.
- A Eulerian trail will exist if the graph:
- Is connected.
- Has exactly two vertices with an odd degree.
- Eulerian trails are useful in situations where every edge must be visited, for example when planning a mail route.
- A Eulerian trail will start from one of the odd vertices.