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Matching Theory. This book surveys matching theory, with an emphasis on connections with other areas of mathematics and on the role matching theory has played, and continues to play, in the development of some of these areas. Besides basic results on the existence of matchings and on the matching structure of graphs, the impact of matching theory is discussed by providing crucial special cases and nontrivial examples on matroid theory, algorithms, and polyhedral combinatorics.
The new Appendix outlines how the theory and applications of matching theory have continued to develop since the book was first published in , by launching among other things the Markov Chain Monte Carlo method. Size and structure. Bipartite graphs with perfect matehinga. General graphs with perfect matchings.
Some graphtheoretical problems. Box 6A Reducibility problems. Matching and linear programming. The f factor problem. Matroid matching. Vertex packing and covering. Developments in matching theory since. Index of Terms. Index of Symbols. Errata in the book. Determinants and matchings. Plummer , L. Plummer American Mathematical Soc. Matchings in bipartite graphs.
Flow theory. Matching Theory M.
Additional Material for the Book
I always have exactly one bed-time mathematical book to read for an hour before going to sleep. It helps me learn new concepts and hopefully stumble upon interesting open problems. I bought this book 3 years back during my PhD days but never got a chance to read it. I guess they are printing it on-demand. If you are interested in learning the algorithmic and combinatorial foundations of Matching Theory with a historic perspective , then this book is a must read. If you know the status or progress of these problems, please leave a comment. The toughness of a graph , is defined to be , if and to be , if.
Matching Theory, Volume 29
Matchings in Bipartite Graphs. Hall and Frobenius. Deficiency, Surplus and a Glimpse of Matroid Theory. Some Consequences of Bipartite Matching Theorems.