An Eulerian path, also called an Euler chain, Euler trail, Euler walk, or "Eulerian" version of any of these variants, is a walk on the graph edges of a graph which uses each graph edge in the original graph exactly once. A connected graph has an Eulerian path iff it has at most two graph vertices of odd degree.

# Eulerian Path

## See also

Eulerian Cycle, Eulerian Graph, Hamiltonian Cycle, Hamiltonian Path, Königsberg Bridge Problem, Path, Walk## Explore with Wolfram|Alpha

## References

Edmonds, J. and Johnson, E. L. "Matching, Euler Tours, and the Chinese Postman."*Math. Programm.*

**5**, 88-124, 1973.Wilson, R. J. "An Eulerian Trail through Königsberg."

*J. Graph Th.*

**10**, 265-275, 1986.

## Referenced on Wolfram|Alpha

Eulerian Path## Cite this as:

Weisstein, Eric W. "Eulerian Path." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/EulerianPath.html