(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
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.
If you have suggestions, corrections, or comments, please get in touch with Paul Black.
Entry modified 2 September 2014.
HTML page formatted Mon Feb 2 13:10:39 2015.
Cite this as:
Paul E. Black, "Euler cycle", in
Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 2 September 2014. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/eulercycle.html