Some Topics In Matroid Theory
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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.
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.
Matroid Theory
Author: D. J. A. Welsh
language: en
Publisher: Courier Corporation
Release Date: 2010-01-01
The theory of matroids connects disparate branches of combinatorial theory and algebra such as graph and lattice theory, combinatorial optimization, and linear algebra. This text describes standard examples and investigation results, and it uses elementary proofs to develop basic matroid properties before advancing to a more sophisticated treatment. 1976 edition.