Factors and Factorizations of Graphs
Proof Techniques in Factor Theory
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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.
Inhaltsverzeichnis
1 Basic Terminology. - 2 Matchings and 1-Factors. - 3 Regular Factors and f-Factors. - 4 (g, f)-Factors and [a, b]-Factors. - 5 [a, b]-Factorizations. - 6 Parity Factors. - 7 Component Factors. - 8 Spanning Trees.
Produktdetails
Erscheinungsdatum
23. Juni 2011
Sprache
englisch
Auflage
2011
Seitenanzahl
368
Reihe
Lecture Notes in Mathematics
Autor/Autorin
Jin Akiyama, Mikio Kano
Verlag/Hersteller
Produktart
kartoniert
Abbildungen
XII, 353 p. 153 illus.
Gewicht
557 g
Größe (L/B/H)
235/155/20 mm
ISBN
9783642219184
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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)
"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)
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