Introduction to the Theory of Matroids PDF Download

Author: Rabe Randow
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 124

View

Book Description

Author: Gary Gordon
Publisher: Cambridge University Press
ISBN: 1139536087
Category : Mathematics
Languages : en
Pages : 406

View

Book Description
Matroid theory is a vibrant area of research that provides a unified way to understand graph theory, linear algebra and combinatorics via finite geometry. This book provides the first comprehensive introduction to the field which will appeal to undergraduate students and to any mathematician interested in the geometric approach to matroids. Written in a friendly, fun-to-read style and developed from the authors' own undergraduate courses, the book is ideal for students. Beginning with a basic introduction to matroids, the book quickly familiarizes the reader with the breadth of the subject, and specific examples are used to illustrate the theory and to help students see matroids as more than just generalizations of graphs. Over 300 exercises are included, with many hints and solutions so students can test their understanding of the materials covered. The authors have also included several projects and open-ended research problems for independent study.

Author: W. T. Tutte
Publisher:
ISBN:
Category : Matroids
Languages : en
Pages : 98

View

Book Description
The basic concepts and methods of matroid theory are presented. The Memorandum defines a matroid axiomatically and introduces the matroids associated with the structures of graphs and chain-groups. It discusses the subgraphs and contractions of a graph, exhibits corresponding simplifications of chain-groups and matroids, and studies the rank of a matroid. It also examines a property of matroids called connection and shows that it corresponds to the property of nonseparability for graphs. It further treats the detailed structure of a matroid (that is, it studies the relation between a given circuit and the rest of the matroid), and concludes by considering the regular matroids and their associated chain-groups. The regular matroids mark an interesting half-way stage between the matroids corresponding to graphs on the one hand, and the binary matroids, corresponding to chain-groups over GF(2), on the other. (Author).