Topics in Matroid Theory

Leonidas S. Pitsoulis (Autor)

Buch | Softcover

127 Seiten

2013
Springer-Verlag New York Inc.
978-1-4614-8956-6 (ISBN)

Artikel merken

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.

1.Introduction.- 2.Graph Theory, Vector Spaces and Transversals.- 3.Definition of Matroids.- 4.Representability, Duality, Minors, and Connectivity.- 5. Decomposition of Graphic Matroids.- 6.Signed-Graphic Matroids.- List of Symbols.- Index.

Reihe/Serie	SpringerBriefs in Optimization
Zusatzinfo	46 Illustrations, black and white; XIV, 127 p. 46 illus.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Graphentheorie
Schlagworte	combinatorial geometries • combinatorial optimization • Matroid Theory • recognition algorithm • union algorithms
ISBN-10	1-4614-8956-3 / 1461489563
ISBN-13	978-1-4614-8956-6 / 9781461489566
Zustand	Neuware