Simple chain that passes through all of the edges in an undirected graph.

### Property

A graph contains a Eulerian chain if the graph is connected and if it has two vertices of odd order.

### Example

In this graph, there is no Eulerian chain because there are more than two vertices of odd order.

The graph below has a Eulerian chain following the vertices in this order: B – A – E – D – C – B – E.

Note that the Eulerian chain above starts at an odd order vertex (B) and ends at the other odd order vertex (E).