Ebook: Matroid Theory and its Applications in Electric Network Theory and in Statics
Author: András Recski (auth.)
- Tags: Combinatorics, Geometry, Topology, Appl.Mathematics/Computational Methods of Engineering, Electrical Engineering
- Series: Algorithms and Combinatorics 6
- Year: 1989
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
I. The topics of this book The concept of a matroid has been known for more than five decades. Whitney (1935) introduced it as a common generalization of graphs and matrices. In the last two decades, it has become clear how important the concept is, for the following reasons: (1) Combinatorics (or discrete mathematics) was considered by many to be a collection of interesting, sometimes deep, but mostly unrelated ideas. However, like other branches of mathematics, combinatorics also encompasses some gen eral tools that can be learned and then applied, to various problems. Matroid theory is one of these tools. (2) Within combinatorics, the relative importance of algorithms has in creased with the spread of computers. Classical analysis did not even consider problems where "only" a finite number of cases were to be studied. Now such problems are not only considered, but their complexity is often analyzed in con siderable detail. Some questions of this type (for example, the determination of when the so called "greedy" algorithm is optimal) cannot even be answered without matroidal tools.
Content:
Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Basic concepts from graph theory....Pages 3-36
Applications....Pages 37-68
Planar graphs and duality....Pages 69-91
Applications....Pages 92-106
The theorems of K?nig and Menger....Pages 107-130
Applications....Pages 131-147
Front Matter....Pages 149-149
Basic concepts in matroid theory....Pages 151-170
Applications....Pages 171-184
Algebraic and geometric representation of matroids....Pages 185-205
Applications....Pages 206-221
The sum of matroids I....Pages 222-232
Applications....Pages 233-246
The sum of matroids II....Pages 247-259
Applications....Pages 260-272
Matroids induced by graphs....Pages 273-286
Applications....Pages 287-292
Some recent results in matroid theory....Pages 293-306
Applications....Pages 307-316
Back Matter....Pages 317-533
Content:
Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Basic concepts from graph theory....Pages 3-36
Applications....Pages 37-68
Planar graphs and duality....Pages 69-91
Applications....Pages 92-106
The theorems of K?nig and Menger....Pages 107-130
Applications....Pages 131-147
Front Matter....Pages 149-149
Basic concepts in matroid theory....Pages 151-170
Applications....Pages 171-184
Algebraic and geometric representation of matroids....Pages 185-205
Applications....Pages 206-221
The sum of matroids I....Pages 222-232
Applications....Pages 233-246
The sum of matroids II....Pages 247-259
Applications....Pages 260-272
Matroids induced by graphs....Pages 273-286
Applications....Pages 287-292
Some recent results in matroid theory....Pages 293-306
Applications....Pages 307-316
Back Matter....Pages 317-533
....