Constructing Eulerian Cycles and Paths from Euler’s Theorem

Let’s construct Eulerian cycles and paths by using Euler’s theorem.

Algorithm for finding an Eulerian cycle

The proof of Euler’s Theorem offers an example of what mathematicians call a constructive proof, which not only proves the desired result but also provides us with a method for constructing the object we need. In short, we track Leo’s movements until he inevitably produces an Eulerian cycle in a balanced and strongly connected graph Graph, as summarized in the following pseudocode.

We’ll also take a look at the following function that will generate Eulerian Cycles.

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