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＜電子ブック＞
Topics in Matroid Theory / by Leonidas S. Pitsoulis
(SpringerBriefs in Optimization. ISSN:2191575X)

版	1st ed. 2014.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2014
本文言語	英語
大きさ	XIV, 127 p. 46 illus : online resource
著者標目	*Pitsoulis, Leonidas S author SpringerLink (Online service)
件　名	LCSH:Mathematical optimization LCSH:Algorithms LCSH:Discrete mathematics LCSH:Graph theory LCSH:Geometry FREE:Continuous Optimization FREE:Algorithms FREE:Discrete Mathematics FREE:Graph Theory FREE:Geometry
一般注記	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 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.   HTTP:URL=https://doi.org/10.1007/978-1-4614-8957-3

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