# Combinatorial Problems and Exercises

American Mathematical Soc., 1993 - Mathematics - 639 pages
The main purpose of this book is to provide help in learning existing techniques in combinatorics. The most effective way of learning such techniques is to solve exercises and problems. This book presents all the material in the form of problems and series of problems (apart from some general comments at the beginning of each chapter). In the second part, a hint is given for each exercise, which contains the main idea necessary for the solution, but allows the reader to practice theechniques by completing the proof. In the third part, a full solution is provided for each problem. This book will be useful to those students who intend to start research in graph theory, combinatorics or their applications, and for those researchers who feel that combinatorial techniques mightelp them with their work in other branches of mathematics, computer science, management science, electrical engineering and so on. For background, only the elements of linear algebra, group theory, probability and calculus are needed.

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### Contents

 III 15 IV 22 V 29 VI 33 VII 40 VIII 45 IX 55 X 62
 XXIX 147 XXX 148 XXXI 153 XXXII 156 XXXIII 161 XXXIV 200 XXXV 225 XXXVI 246

 XI 65 XII 72 XIII 78 XIV 87 XV 90 XVI 98 XVII 103 XVIII 109 XIX 113 XX 116 XXI 118 XXII 122 XXIII 124 XXIV 130 XXV 133 XXVI 135 XXVII 138 XXVIII 142
 XXXVII 281 XXXVIII 303 XXXIX 341 XL 380 XLI 392 XLII 422 XLIII 452 XLIV 493 XLV 512 XLVI 552 XLVII 581 XLVIII 605 XLIX 621 L 625 LI 627 LII 631 LIII 637 Copyright

### Popular passages

Page 45 - A graph is planar if and only if it contains no subdivision of...
Page 18 - A(n) is the number of partitions of n into an even number of distinct parts and B(n) is the number of partitions of n into an odd number of distinct parts.
Page 31 - Along a speed track there are some gas-stations. The total amount of gasoline available in them is equal to what our car (which has a very large tank) needs for going around the track. Prove that there is a gas-station such that if we start there with an empty tank, we shall be able to go around the track without running out of gasoline.
Page 11 - Those techniques whose absence has been disapproved of above await their discoverers. So underdevelopment is not a case against, but rather for, directing young scientists toward a given field.
Page 9 - I could not resist, however, to working out a series of exercises on random walks on graphs, and their relations to eigenvalues, expansion properties, and electrical resistance (this area has classical roots but has grown explosively in the last few years).
Page 11 - As long as the main questions have not been formulated and the abstractions to a general level have not been carried through, there is no way to distinguish between interesting and less interesting results — except on an aesthetic basis, which is, of course, too subjective.

### References to this book

 Approximation AlgorithmsVijay V. VaziraniLimited preview - 2002
 The Design of Innovation: Lessons from and for Competent Genetic AlgorithmsDavid Edward GoldbergNo preview available - 2002
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