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Lecture Notes in Mathematics

Factors and Factorizations of Graphs

Proof Techniques in Factor Theory

Authors: Akiyama, Jin, Kano, Mikio

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  • The book is self-contained and comprehensive, allowing readers to rely on it exclusively to understand the entire history and development of this area.
  •  Unlike other books, in which difficult proof techniques are simply lifted from earlier sources, in this book, the contents of each proof technique is analyzed and streamlined.
  • Each chapter features conjectures and open problems, inspiring readers to further their own study.
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  • ISBN 978-3-642-21919-1
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Softcover 67,59 €
price for Spain (gross)
  • ISBN 978-3-642-21918-4
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About this book

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.

Reviews

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 Kano’s 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)


Table of contents (8 chapters)

Table of contents (8 chapters)
  • Basic Terminology

    Pages 1-14

    Akiyama, Jin (et al.)

  • Matchings and 1-Factors

    Pages 15-67

    Akiyama, Jin (et al.)

  • Regular Factors and f-Factors

    Pages 69-141

    Akiyama, Jin (et al.)

  • (g, f)-Factors and [a, b]-Factors

    Pages 143-191

    Akiyama, Jin (et al.)

  • [a, b]-Factorizations

    Pages 193-218

    Akiyama, Jin (et al.)

Buy this book

eBook 53,54 €
price for Spain (gross)
  • ISBN 978-3-642-21919-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 67,59 €
price for Spain (gross)
  • ISBN 978-3-642-21918-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Factors and Factorizations of Graphs
Book Subtitle
Proof Techniques in Factor Theory
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2031
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-21919-1
DOI
10.1007/978-3-642-21919-1
Softcover ISBN
978-3-642-21918-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XII, 353
Number of Illustrations
153 b/w illustrations
Topics