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《圖的因子和匹配可擴性》講述瞭：Graph theory is one of the branches of modern mathematics which has shown impressive ad vances in recet years.An explosive growth of graph theory is witnessed due to its essential roles providing structural and indispens-able tools in computer science,communication networks and combinatorial optimization problems.

Dr.Yu is a professor in the Department of Mathematics and Statistics at the Thompson Rivers University of Canada.His research interests include graph theory and combinatorial optimization.

Dr.Liu is a professor in the School of Mathematics at Shandong University of China.Her research interests include graph theory and matroid theory.

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
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