# Euler cycle

(definition)

**Definition:**
A *path* through a *graph* which starts and ends at the same *vertex* and includes every *edge* exactly once.

**Also known as** Eulerian path, Königsberg bridges problem.

**Aggregate parent** (I am a part of or used in ...)

*Christofides algorithm*.

**See also**
*Hamiltonian cycle*, *Chinese postman problem*.

*Note:
"Euler" is pronounced "oil-er". A Hamiltonian cycle includes each vertex once; an Euler cycle includes each edge once.*

Author: PEB

## Implementation

(Mathematica and Fortran)
## More information

examples and explanations

**Historical Note**

Euler defined the cycle to solve the puzzle of finding a path across every bridge of the German city of Königsberg exactly once.

Go to the
Dictionary of Algorithms and Data
Structures home page.

If you have suggestions, corrections, or comments, please get in touch
with Paul Black.

Entry modified 24 August 2017.

HTML page formatted Fri Feb 23 10:06:07 2018.

Cite this as:

Paul E. Black, "Euler cycle", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 24 August 2017. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/eulercycle.html