Abstract

This study of matching theory deals with bipartite matching, network flows, and presents fundamental results for the non-bipartite case. It goes on to study elementary bipartite graphs and elementary graphs in general. Further discussed are 2-matchings, general matching problems as linear programs, the Edmonds Matching Algorithm (and other algorithmic approaches), f-factors and vertex packing.
It begins at an elementary level and ends at the frontiers of current research, and the journey is enlivened by readable exposition, helpful motivation, interesting historical background and elegant proofs... a truly notable achievement...
Bulletin of the London Mathematical Society
Everything is developed with splendid clarity, organized in a masterful way and written in an excellent style, sometimes exciting, sometimes humorous, always maintaining a lively dialogue with the reader. This beautiful book provides a comprehensive treatment of the subject, leading up to the frontiers of current research.
Optima