图的因子和匹配可扩性

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 k-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 k-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
6.3.1 Matching extension and forbidden subgraphs
6.3.2 Matching extension and toughness
6.3.3 Matching extension in planar graphs and surfaces
6.3.4 Matching extension，degree sum and closure operations
6.3.5 Matching extension and product of graphs
6.3.6 Matching extension and other parameters
6.4 Extendability of symmetric graphs
7 Extremal k-Extendable Graphs and Generalizations
7.1 Maximal and minimal k-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