Advertisement

© 2011

Factors and Factorizations of Graphs

Proof Techniques in Factor Theory

  • 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.

Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2031)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Jin Akiyama, Mikio Kano
    Pages 1-14
  3. Jin Akiyama, Mikio Kano
    Pages 15-67
  4. Jin Akiyama, Mikio Kano
    Pages 69-141
  5. Jin Akiyama, Mikio Kano
    Pages 143-191
  6. Jin Akiyama, Mikio Kano
    Pages 193-218
  7. Jin Akiyama, Mikio Kano
    Pages 219-251
  8. Jin Akiyama, Mikio Kano
    Pages 253-293
  9. Jin Akiyama, Mikio Kano
    Pages 295-336
  10. Back Matter
    Pages 337-356

About this book

Introduction

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.

Keywords

05C; 05CXX; 05C75 Factorizations of Graphs Factors of Graphs Matchings in Graphs Proof Technique

Authors and affiliations

  1. 1.Research Institute, of Educational DevelopmentTokai UniversityShibuya-kuJapan
  2. 2.Computer and Information SciencesIbaraki UniversityHitachiJapan

Bibliographic information

  • Book Title Factors and Factorizations of Graphs
  • Book Subtitle Proof Techniques in Factor Theory
  • Authors Jin Akiyama
    Mikio Kano
  • Series Title Lecture Notes in Mathematics
  • DOI https://doi.org/10.1007/978-3-642-21919-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-642-21918-4
  • eBook ISBN 978-3-642-21919-1
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages XII, 353
  • Number of Illustrations 153 b/w illustrations, 0 illustrations in colour
  • Topics Mathematics, general
    Programming Techniques
  • Buy this book on publisher's site
Industry Sectors
Aerospace
Automotive
Finance, Business & Banking

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)