Matroid theory / D.J.A. Welsh.

Originally published: New York : Academic Press, 1976.

Includes bibliographical references and index.

Fundamental concepts and examples -- Duality -- Lattice theory and matroids -- Submatroids -- Matroid connection -- Matroids, graphs and planarity -- Transversal theory -- Covering and packing -- The vector representation of matroids -- Binary matroids -- Matroids from fields and groups -- Block designs and matroids -- Menger's theorem and linkings in graphs -- Transversal matroids and related topics -- Polynomials, colouring problems, codes and packings -- Extremal problems -- Maps between matroids and geometric lattices -- Convex polytopes associated with matroids -- Combinatorial optimisation -- Infinite structures.

"The theory of matroids connects disparate branches of combinatorial theory and algebra such as graph and lattice theory, combinatorial optimization, and linear algebra. Aimed at advanced undergraduate and graduate students, this text is one of the earliest substantial works on matroid theory. Its author, D.J.A. Welsh, Professor of Mathematics at Oxford University, has exercised a profound influence over the theory's development. The first half of the text describes standard examples and investigation results, using elementary proofs to develop basic matroid properties and referring readers to the literature for more complex proofs. The second half advances to a more sophisticated treatment, addressing a variety of research topics. Praised by the Bulletin of the American Mathematical Society as 'a useful resource for both the novice and the expert', this text features numerous helpful exercises."--Publisher's description.