Factors and Factorizations of Graphs Proof Techniques in Factor Theory [Paperback]

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.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.

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 andlC.