Topics In Matroid Theory
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Topics in Matroid Theory
Author: Leonidas S. Pitsoulis
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-10-24
Topics in Matroid Theory provides a brief introduction to matroid theory with an emphasis on algorithmic consequences.Matroid theory is at the heart of combinatorial optimization and has attracted various pioneers such as Edmonds, Tutte, Cunningham and Lawler among others. Matroid theory encompasses matrices, graphs and other combinatorial entities under a common, solid algebraic framework, thereby providing the analytical tools to solve related difficult algorithmic problems. The monograph contains a rigorous axiomatic definition of matroids along with other necessary concepts such as duality, minors, connectivity and representability as demonstrated in matrices, graphs and transversals. The author also presents a deep decomposition result in matroid theory that provides a structural characterization of graphic matroids, and show how this can be extended to signed-graphic matroids, as well as the immediate algorithmic consequences.
Matroids: A Geometric Introduction
Author: Gary Gordon
language: en
Publisher: Cambridge University Press
Release Date: 2012-08-02
This friendly introduction helps undergraduate students understand and appreciate matroid theory and its connections to geometry.
Matroid Theory
This major revision of James Oxley's classic Matroid Theory provides a comprehensive introduction to the subject, covering the basics to more advanced topics. With over 700 exercises and proofs of all relevant major theorems, this book is the ideal reference and class text for academics and graduate students in mathematics and computer science.