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-factors2 Degree Constraint Factors 2.1 Characterizations of factors 2.2 Factors in bipartite graphs 2.3 Factors with special properties 2.4 L-factor3 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 factors4 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 trees5 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 decomposition6 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 graphs7 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 extension8 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 factorsIndexReferences
· · · · · · (收起)