Topic summary
Euler tour
Extracted from the Wikipedia article Eulerian path.
Definition
An Eulerian cycle, also called an Eulerian circuit or Euler tour, in an undirected graph is a circuit that uses each edge exactly once. If such a cycle exists, the graph is called Eulerian or unicursal. The term "Eulerian graph" is also sometimes used in a weaker sense to denote a graph where every vertex has even degree. For finite connected graphs the two definitions are equivalent, while a possibly unconnected graph is Eulerian in the weaker sense if and only if each connected component has an Eulerian cycle.