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E-raamat: Factors and Factorizations of Graphs: Proof Techniques in Factor Theory

  • Formaat: PDF+DRM
  • Sari: Lecture Notes in Mathematics 2031
  • Ilmumisaeg: 21-Jun-2011
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783642219191
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  • Formaat: PDF+DRM
  • Sari: Lecture Notes in Mathematics 2031
  • Ilmumisaeg: 21-Jun-2011
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783642219191

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This book chronicles the development of graph factors and factorizations. It pursues a comprehensive approach, addressing most of the important results from hundreds of findings over the last century. One of the main themes is the observation that many theorems can be proved using only a few standard proof techniques. This stands in marked contrast to the seemingly countless, complex proof techniques offered by the extant body of papers and books. In addition to covering the history and development of this area, the book offers conjectures and discusses open problems. It also includes numerous explanatory figures that enable readers to progressively and intuitively understand the most important notions and proofs in the area of factors and factorization.

Arvustused

From the reviews:

The book covers such central topics of the theory of graph factorization as matchings, regular factors, f-factors, (g. f)-factors, [ a,b]-factorisation. great value to graduate students and researchers in graph theory. The book is written very carefully and in clear style, and it contains numerous figures illustrating key notions. Akiyama and Kanos book makes a great contribution to furthering the study of graph factorization by collecting and exhibiting some of the most important concepts and results obtained since the nineteen eighties. (Anders Sune Pedersen, Zentralblatt MATH, Vol. 1229, 2012)

Many theorems in this book can be proved using only a few standard proof techniques, which makes it very easy for readers to understand factors and factorizations of graphs. Furthermore, many detailed illustrations are given to accompany the proofs. This book is comprehensive and covers most of the important results since 1980. Hence, it provides much worthwhile information to readers. (Sizhong Zhou, Mathematical Reviews, Issue 2012 k)

1 Basic Terminology
1(14)
Problems
14(1)
2 Matchings and 1-Factors
15(54)
2.1 Matchings in bipartite graphs
15(9)
2.2 Covers and transversals
24(7)
2.3 Augmenting paths and algorithms
31(5)
2.4 1-factor theorems
36(8)
2.5 Graphs having 1-factors
44(12)
2.6 Structure theorem
56(6)
2.7 Algorithms for maximum matchings
62(3)
2.8 Perfect matchings in cubic graphs
65(4)
Problems
66(3)
3 Regular Factors and f-Factors
69(74)
3.1 The f-factor theorem
69(9)
3.2 Regular factors in regular graphs
78(13)
3.3 Regular factors and f-factors in graphs
91(39)
3.4 Regular factors and f-factors in bipartite graphs
130(13)
Problems
141(2)
4 (g, f)-Factors and [ a, b]-Factors
143(50)
4.1 The (g, f)-factor theorem
143(14)
4.2 Graphs having the odd-cycle property
157(6)
4.3 [ a, b]-factors and (g, f)-factors
163(30)
Problems
190(3)
5 [ a, b]-Factorizations
193(26)
5.1 Factorizations of special graphs
193(5)
5.2 Semi-regular factorization
198(5)
5.3 [ a, b]-factorizations of graphs
203(16)
6 Parity Factors
219(34)
6.1 Parity (g, f)-factors and (1, f)-odd factors
219(7)
6.2 (1, f)-odd subgraphs and structure theorem
226(16)
6.3 Partial parity (g, f)-factors and coverings
242(8)
6.4 H-factors
250(3)
Problems
251(2)
7 Component Factors
253(42)
7.1 Path factors and star factors
253(33)
7.2 Cycle factors and other component factors
286(9)
Problems
293(2)
8 Spanning Trees
295(42)
8.1 Preliminaries and minimum spanning trees
295(3)
8.2 Spanning k-trees
298(13)
8.3 Spanning k-ended tree
311(15)
8.4 Spanning trees with miscellaneous properties
326(11)
References 337(11)
Glossary of functions 348(1)
Glossary of notation 349(2)
Index 351