Matroid Theory - Rilegato

Oxley, James G.

Rilegato

ISBN 10: 0198535635 ISBN 13: 9780198535638

Casa editrice: OUP Oxford, 2001

Riassunto

What is the essence of the similarity between forests in a graph and linearly independent sets of columns in a matrix? Why does the greedy algorithm produce a spanning tree of minimum weight in a connected graph? Is it possible to test in polynomial time whether a matrix is totally unimodular? These questions form the basis of Matroid theory. The study of matroids is a branch of discrete mathematics with basic links to graphs, lattices, codes, transversals, and projective geometries. Matroids are of fundamental importance in combinatorial optimization and their applications extend into electrical engineering and statics. This book falls into two parts: the first provides a comprehensive introduction to the basics of matroid theory, while the second treats more advanced topics. The book contains over five hundred exercises and includes, for the first time in one place, short proofs of all but one of the major theorems in the subject. The final chapter lists sixty unsolved problems and describes progress towards their solutions.

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L'autore:

James Oxley was born in Australia. After completing his undergraduate studies there, he received his doctorate from Oxford University in 1978 under the supervision of Dominic Welsh. After a postdoctoral position at the Australian National University and a Fulbright Postdoctoral Fellowship at the University of North Carolina, he began working at Louisiana State University in 1982. He has been an Alumni Professor there since 1999. He has written more than one hundred research papers in matroid theory and graph theory and has given over fifty conference talks including plenary addresses at the British Combinatorial Conference in 2001 and an American Mathematical Society meeting in 2002. Fourteen students have completed doctorates under his supervision and he is currently advising five other doctoral candidates. In 1999, he was named L.S.U's Distinguished Research Master for Engineering, Science, and Technology. From April until July 2005, he was a Visiting Research Fellow at Merton College, Oxford.

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Su questa edizione

• Editore: OUP Oxford
• Data di pubblicazione: 2001
• ISBN 10: 0198535635
• ISBN 13: 9780198535638
• Rilegatura: Copertina rigida
• Numero di pagine: 544