James G. Oxley.
Matroid Theory.
OUP. 1992
The study of matroids is a branch of discrete mathematics
with basic links to graphs, lattices, codes, transversals, and projective geometries.
Matroids are of fundamental importance in combinatorial optimization
and their applications extend into electrical engineering and statics.
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. The book contains over five hundred exercises and includes, for the first time in one place, short proofs of all but one of the major theorems in the subject. The final chapter lists sixty unsolved problems and describes progress towards their solutions.