Euler & Hamilton Paths

Euler path is another term for Euler walk. Below are several examples of graphs to try your hand at finding an Euler path. Just click on the nodes in sequence. As you progress, the edges you passed over will disappear. But do not worry. When you are finished they will appear again in a different color.

You may choose to seek a Hamilton path instead. Hamilton path is a path that passes through every vertex of a graph exactly once. A Hamiltonian path which is also a loop is called Hamilton (or Hamiltonian) cycle. The motions are about the same, but the algorithms are entirely different.

(There is a very nice puzzle whose solution depends on existence or absence of a Hamiltonian path on a graph. There are also separate applets for practicing Euler and Hamilton paths. Both have the facility to help create graphs online.)

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