Quotes About Graph Theory

Map coloring problem. Find the smallest number m such that the faces of every planar graph can be colored with m or fewer colors in such a way that faces sharing a border have different colors.

THE ACYCLIC DEPENDENCIES PRINCIPLE Allow no cycles in the component dependency graph.

A calculation, in fact, demonstrates that without nodes, physical space has no volume. In other words, it is in the nodes of the graph, not in the lines, that the volume of space "resides." The lines "link together" individual volumes sitting at the nodes.

Anytime you want to hear about graph partitioning, I will be glad to tell you what I know about graph partitioning. It remains a standard problem. I think it's an interesting problem, because it shows up in a variety of guises in real life.