It is also possible to use the depth-first search to linearly order the vertices of the original graph (or tree).

This is valid because we only merged vertices that were not adjacent in the original graph.

In the third and last phase, the computed partition is iteratively projected back to the original graph.

The software simply assigns a coordinate system to the pixels in the image based upon the scaling values entered from the original graph.

In the former case, if M has a red K then so does the original graph and we are finished.

Since the original graph had minimum degree 5, each endpoint of a new edge has degree at least 6.

Thus, if the triangulation contains a light edge, then that edge must have been in the original graph.

It is called the medial graph of the 4-valent original graph.

In the meantime - just pretend the original graph is a record of the Italian bond spreads (only less alarming).

If the final graph consists of a single node, then the original graph is said to be reducible.