Matroid Theory

Abstract Seventy-five years of the study of matroids has seen the development of a rich theory with links to graphs, lattices, codes, transversals,0020and projective geometries. Matroids are of fundamental importance in combinatorial optimization and their applications extend into electrical and structural engineering. This book falls into two parts: the first provides a comprehensive introduction to the basics of matroid theory, while the second treats more advanced topics. It contains over 700 exercises, and includes proofs of all of the major theorems in the subject. The last two chapters review current research and list more than eighty unsolved problems along with a description of the progress towards their solutions.