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 (Java, C++, and Mathematica)
Euler defined the cycle to solve the puzzle of finding a path across every bridge of the German city of Königsberg exactly once.
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Entry modified 2 November 2020.
HTML page formatted Mon Nov 2 12:36:42 2020.
Cite this as:
Paul E. Black, "Euler cycle", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 2 November 2020. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/eulercycle.html