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Factors and Factorizations of Graphs

Proof Techniques in Factor Theory

  • Book
  • © 2011

Overview

Authors:
  1. Jin Akiyama

    1. Research Institute, of Educational Development, Tokai University, Shibuya-ku, Japan

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    You can also search for this author in PubMed   Google Scholar

  2. Mikio Kano

    1. Computer and Information Sciences, Ibaraki University, Hitachi, Japan

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    You can also search for this author in PubMed   Google Scholar

  • 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.
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
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  2. Basic Terminology

    • Jin Akiyama, Mikio Kano
    Pages 1-14

  3. Matchings and 1-Factors

    • Jin Akiyama, Mikio Kano
    Pages 15-67

  4. Regular Factors and f-Factors

    • Jin Akiyama, Mikio Kano
    Pages 69-141

  5. (g, f)-Factors and [a, b]-Factors

    • Jin Akiyama, Mikio Kano
    Pages 143-191

  6. [a, b]-Factorizations

    • Jin Akiyama, Mikio Kano
    Pages 193-218

  7. Parity Factors

    • Jin Akiyama, Mikio Kano
    Pages 219-251

  8. Component Factors

    • Jin Akiyama, Mikio Kano
    Pages 253-293

  9. Spanning Trees

    • Jin Akiyama, Mikio Kano
    Pages 295-336

  10. Back Matter

    Pages 337-356
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Keywords

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)

Authors and Affiliations

  • Research Institute, of Educational Development, Tokai University, Shibuya-ku, Japan

    Jin Akiyama

  • Computer and Information Sciences, Ibaraki University, Hitachi, Japan

    Mikio Kano

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

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2011

  • Softcover ISBN: 978-3-642-21918-4Published: 23 June 2011

  • eBook ISBN: 978-3-642-21919-1Published: 21 June 2011

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 353

  • Number of Illustrations: 153 b/w illustrations

  • Topics: Mathematics, general, Programming Techniques

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