Perfect Matchings: A Theory of Matching Covered Graphs

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.

Cláudio Leonardo Lucchesi graduated from the University of Sao Paulo in 1968 with a degree in Electrical Engineering. He then went to the University of Waterloo in Canada with the intention of doing a doctorate in Computer Science. But, attracted by a conjectured minimax relation, he switched to graph theory, worked under the guidance of Daniel H Younger, and obtained his PhD degree in 1976. Returning to Brazil, he taught for a number of years in the Department of Computer Science at the State University of Campinas. After retirement in 2001, and after a short tenure at the Federal University of Mato Grosso do Sul, he is now happily back at his alma mater.

U.S.R. Murty learned graph theory from Professor Claude Berge and finished his PhD at the Indian Statistical Institute under the supervision of the well-known statistician Dr. C.R. Rao. He has been at the University of Waterloo, Canada, since 1967. He co-authored two books on graph theory with J.A. Bondy (Graph Theory with Applications, Macmillan, 1976; and Graph Theory, Springer, 2008.