(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

examples and explanations (Java, C++, and Mathematica)

**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 12 August 2019.

HTML page formatted Mon Aug 12 09:59:40 2019.

Cite this as:

Paul E. Black, "Euler cycle", in
*Dictionary of Algorithms and Data Structures* [online], Paul E. Black, ed. 12 August 2019. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/eulercycle.html