Contents Preface Notations Chapter 1 Introduction and Main Results 1.1 Basic concepts and definitions 1.2 Invariants for 2-factors in graphs 1.3 Degree condition for 2-factors in bipartite graphs 1.4 Invariants for vertex-disjoint cycles in graphs 1.5 Invariants for vertex-disjoint cycles with constraints 1.5.1 Degree conditions for vertex-disjoint cycles containing prescribed elements 1.5.2 Degree conditions for vertex-disjoint cycles with length constraints in digraphs 1.5.3 Degree conditions for vertex-disjoint cycles with length constraints in tournaments 1.6 Outline the main results Chapter 2 Neighborhood Unions for Disjoint Chorded Cycles in Graphs 2.1 Introduction 2.2 Basic induction 2.3 Proof of Theorem 2.4 Chapter 3 Vertex-Disjoint Double Chorded Cycles in Bipartite Graphs 3.1 Introduction 3.2 Lemmas 3.3 Proof of Theorem 3.5 Chapter 4 2-Factors with Specified Elements in Graphs 4.1 2-Factors with chorded quadrilaterals 4.1.1 Lemmas 4.1.2 Proof of Theorem 4.2 4.2 2-Factors Containing Specified Vertices in A Bipartite Graph 4.2.1 Lemmas 4.2.2 Proof of Theorem 4.6 4.2.3 Proof of Theorem 4.7 4.2.4 Discussion Chapter 5 Packing Triangles and Quadrilaterals 5.1 Introduction and terminology 5.2 Lemmas 5.3 Proof of Theorem 5.3 Chapter 6 Extremal Function for Disjoint Chorded Cycles 6.1 Extremal function for disjoint cycles in graphs 6.2 Proof of Theorem 6.3 6.3 Basic Lemmas 6.4 Proof of Theorem 6.5 6.5 Proof of Theorem 6.9 6.6 Extremal function for disjoint cycles in bipartite graphs 6.7 Lemmas 6.8 Proof of Theorem 6.12 6.9 Proof of Theorem 6.13 6.10 Discussion Chapter 7 Disjoint Cycles in Digraphs and Multigraphs 7.1 Disjoint cycles with di.erent lengths in digraphs 7.2 Disjoint quadrilaterals in digraphs 7.2.1 Introduction 7.2.2 Preliminary Lemmas
7.2.3 Proof of Theorem 7.2 Chapter 8 Vertex-Disjoint Subgraphs with Small Order and Small Minimum Degree 8.1 Disjoint F in K1;4-free graphs with minimum degree at least four 8.1.1 Preparation for the proof of the Theorem 8.4 8.1.2 Proof of the Theorem 8.4 8.2 Disjoint K.4- in claw-free graphs with minimum degree at least five 8.2.1 Definition of several graphs 8.2.2 Preparation for the proof of the Theorem 8.7 8.2.3 Proof of the Theorem 8.7 8.2.4 Discussion References
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