Book of Factors and Factorizations of Graphs

This book was published by Springer (LNM vol.2031) in July 2011. (Approximately 360 pages) Jin Akiyama and Mikio Kano

#### Contents

- 1. Basic Terminology
- Problems

- 2.1 Matchings in Bipartite Graphs
- 2.2 Covers and Transversal
- 2.3 Augmenting Paths and Algorithms
- 2.4 1-Factor Theorems
- 2.5 Graphs Having 1-Factors
- 2.6 Structure Theorem
- 2.7 Algorithms for Maximum Matchings
- Problems

- 3. Regular Factors and f-Factors
- 3.1 The f-Factor Theorem
- 3.2 Regular Factors in Regular Graphs
- 3.3 Regular Factors and f-Factors in Graphs
- 3.4 Regular Factors and f-Factors in Bipartite Graphs
- Problems
- 4. (g, f)-Factors and [a, b]-Factors
- 4.1 The (g, f)-Factor Theorem
- 4.2 Graphs Having the Odd-Cycle Property
- 4.3 [a, b]-Factors and (g, f)-Factors
- Problems
- 5. [a, b]-Factorizations
- 5.1 Factorizations of Special Graphs
- 5.2 Semi-Regular Factorization
- 5.3 [a, b]-Factorizations of Graphs
- Problems
- 6. Parity Factors
- 6.1 Parity (g, f)-Factors and (1, f)-Odd Factors
- 6.2 (1, f)-Odd Subgraphs and Structure Theorem
- 6.3 Partial parity (g, f)-factors and coverings
- 6.4 H-Factors
- Problems
- 7. Component Factors
- 7.1 Path factors and star factors
- 7.2 Cycle factors and other component factors Problems
- Problems
- 8. Spanning trees
- 8.1 Preliminaries and minimum spanning trees
- 8.2 Spanning k-trees
- 8.3 Spanning k-ended trees
- 8.4 Spanning trees with miscellaneous properties

Index