See our review of the third edition (2006) and our note on the release of the fourth edition (2008). Here is the fifth, dated 2012. The rapid pace of updating reflects both the field, which is very active, and the interest in the book, which has been adopted for courses and translated into several languages.
The authors note that when the first edition was written in 2000, the goal was to produce both a usable textbook and a comprehensive reference. Since then, the field has grown so much that attempting to be comprehensive is no longer possible. "If we included everything that we like," the authors say, "the book would grow beyond a single volume." In addition, they note that the fact that the book is being used as a textbook means that "adding some classical material might be more useful than including a selection of latest results."
Additions in this edition include "a proof of Cayley's formula, more details on blocking flows, the new faster b-matching separation algorithm, an approximation scheme for the multidimensional knapsack, and results concerning the multicommodity max-flow min-cut ratio and the sparsest cut problem."
Fernando Q. Gouvêa is the editor of MAA Reviews.