Textbook in PDF format

Beginning with its origins in the pioneering work of W.T. Tutte in 1947, this monograph systematically traces through some of the impressive developments in matching theory.
A graph is matchable if it has a perfect matching. A matching covered graph is a connected graph on at least two vertices in which each edge is covered by some perfect matching. The theory of matching covered graphs, though of relatively recent vintage, has an array of interesting results with elegant proofs, several surprising applications and challenging unsolved problems.
The aim of this book is to present the material in a well-organized manner with plenty of examples and illustrations so as to make it accessible to undergraduates, and also to unify the existing theory and point out new avenues to explore so as to make it attractive to graduate students.
Foreword
Preface
Terminology and Notation
Basic Theory
Perfect Matchings
Matching Covered Graphs
Canonical Partitions
Tight Cuts
Characterizations of Bricks and Braces
The Perfect Matching Polytope
Solid Bricks
Dependence Relation and Removable Classes
Dependence Classes in Bricks
Removable Classes in Solid Bricks
Ear Decompositions
Matching Minors
Brick and Brace Generation
A Conjecture of Lov´asz Concerning Bricks
Robust Cuts in Bricks
b-Invariant Edges in Bricks
The Matching Lattice and Optimal Ear Decompositions
Thin Edges in Bricks and Braces
Strictly Thin Edges in Bricks and Braces
Pfaffian Orientations
Pfaffian Orientations
Similarity of Orientations and Characteristic Orientations
Excluded-Minor Characterizations of Pfaffian Graphs
References
List of Figures
Glossary
Index