Topics in Matroid Theory

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 algebraicframework, thereby providing the analytical tools to solve related difficult algorithmic problems. The monograph contains a rigorousaxiomatic definition of matroids along with other necessary concepts such as duality, minors, connectivity and representability asdemonstrated in matrices, graphs and transversals. The author also presents a deep decomposition result in matroid theory that providesa structural characterization of graphic matroids, and show how this can be extended to signed-graphic matroids, as well as the immediatealgorithmic consequences.