The applet let's you create graphs and practice Fleury's algorithm for finding Euler's paths and cycles.

Under the working tabs (Create Graph and Practice Fleury's Algorithm) the graph you create and work with appears in two copies. The right one is for the illustration purposes only. The graph is created and manipulated exclusively in the left part of the applet.

Create Graph Tab

The edges of the graph are created by dragging the mouse. The vertices are created as needed. For example, if you start or stop the dragging in a vicinity of an existing node, the new edge becomes attached to this vertex. Otherwise, a new vertex is created.

You can always remove the last of your creations (Undo Last) or the entire graph (Reset) and start anew. When ready, move to the Practice Fleury's Algorithm tab.

Practice Fleury's Algorithm Tab

Working with the left copy only, select one vertex at a time and continue to any of the adjacent vertices. (To help you out, the last selected vertex is filled with blue.) By selecting an adjacent vertex, you simultaneously selected an edge joining the two vertices. In the left copy of the graph, the selected edges disappear. In the right copy, they are highlighted in red. In addition, the vertices in the left copy with no attached edges are removed as well.

The process stops when all the edges of the graph have been traversed, implying that the left copy disappears entirely while, in the right copy of the graph, all the edges become highlighted.

Euler's paths and cycles do not exist for every graph. For one, only connected graphs may have either. The same is true for the graphs with the number of odd vertices exceeding 2. These condition are detected on attempts to switch to the Practice Fleury's Algorithm tab. The applet then displays a warning in big red letters. When you see one, please return to the Create Graph tab and fix the error.