Topics in Matroid Theory

ISBN-13: 9781461489566 / Angielski / Miękka / 2013 / 127 str.

Leonidas Pitsoulis

Opis

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.

Recenzje

"The clear and concise style and the well chosen examples illustrating concepts, theorems and algorithms make this book a valuable resource for graduate students and researchers interested in theoretical and algorithmic applications of matroid theory." (Brigitte Servatius, zbMATH 1319.05033, 2015)

"The goal of the book is to introduce a decomposition theorem providing a characterization of graphic and signed-graphic matroids. ... The monograph is recommended basically to master or PhD students. ... The book has a very logical structure which helps the reader to understand the whole issue." (Bálint Márk Vásárhelyi, Acta Scientiarum Mathematicarum, Vol. 80 (3-4), 2014)

Spis treści

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.