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.
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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.
examples and explanations
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 E. Black.
Entry modified 27 October 2005.
HTML page formatted Tue Dec 6 16:16:32 2011.
Cite this as:
Paul E. Black, "Euler cycle", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 27 October 2005. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/eulercycle.html