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 1986, by launching (among other things)
the Markov Chain Monte Carlo method.
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