Topics in Matroid theory
By: Leonidas S. Pitsoulis
Series: SpringerBriefs in Optimization; SpringerBriefs in optimization
Publisher: Springer
Published: 2014
Place of publication: New York
Language: eng
Number of pages: 127
ISBN-13: 9781461489566; 9781461489573
Subjects: Matroids; Algorithms; Computer algorithms
Description: 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.
Notes: Includes bibliographical references (pages 121-124) and index.