Constructing Eulerian Cycles and Paths from 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.