Graph Factors and Matching Extensions deals with two important branches of graph theory factor theory and extendable graphs.Due to the mature techniques and wide ranges of applications，factors and matchings become useful tools in investigation of many theoretical problems and practical issues.This book includes basic techniques，theoretical foundations，as well as recent advances in the field.It also discusses open problems and conjectures to inspire the readers.
This book is primarily aimed at researchers and graduate students in graph theory and combinatorics in general.However，all the necessary prerequisites are developed from scratch and should be accessible to upper level undergraduate students with prior knowledge of graph theory.
- Front Matter
- 1 Matchings and Perfect Matchings
- 1.1 Definitions and terminologies
- 1.2 Matchings in bipartite graphs and augmenting path
- 1.3 Matchings in non-bipartite graphs
- 1.4 Sufficient conditions for 1-factors
- 1.5 Gallai-Edmonds Structure Theorem
- 1.6 Number of 1-factors
- 2 Degree Constraint Factors
- 2.1 Characterizations of factors
- 2.2 Factors in bipartite graphs
- 2.3 Factors with special properties
- 2.4 L-factor
- 3 Factors and Graphic Parameters
- 3.1 Toughness and κ-factors
- 3.2 Toughness and [a,b]-factors
- 3.3 Binding number and factors
- 3.4 Connectivity and factors
- 3.5 Other parameters and existence of factors
- 4 Component Factors and Connected Factors
- 4.1 Star factor
- 4.2 Path and cycle factors
- 4.3 El-Zahar's Conjecture and other component factors
- 4.4 Connected [a,b]-factors
- 4.5 Connected (g,f)-factors
- 4.6 Generalized trees
- 5 Elementary Graphs and Decomposition Theory
- 5.1 Elementary graphs and 1-extendable graphs
- 5.2 Ear decomposition
- 5.3 Minimal graphs and more decompositions
- 5.4 Bricks and optimal ear decomposition
- 6 κ-Extendable Graphs and n-Factor-Critical Graphs
- 6.1 Characterizations and basic properties
- 6.2 Equivalence and recursive relationships
- 6.3 Matching extension and graphic parameters
- 6.4 Extendability of symmetric graphs
- 7 Extremal κ-Extendable Graphs and Generalizations
- 7.1 Maximal and minimal κ-extendable graphs
- 7.2 Generalization of matching extension
- 7.3 Variations of graph extension
- 8 Fractional Factors of Graphs
- 8.1 Fractional matchings
- 8.2 Fractional (g,f)-factors
- 8.3 Parameters and fractional factors of graphs
- 8.4 Maximum and minimum fractional (g,f)-factors
- 8.5 Connected fractional factors
- Index
- References
- 版权
