图的点不交圈问题是著名的哈密尔顿圈及2-因子问题的推广，具有重要的理论价值和实际应用价值，是图论研究的核心问题之一。《Some Topics on Structural Invariants of Vertex-Disjoint Cycles in Graphs》主要研究了图上有限制条件的点不交圈结构参数，主要包括Dirac型*小度参数、极值参数以及邻域并参数，《Some Topics on Structural Invariants of Vertex-Disjoint Cycles in Graphs》得到的这些参数大多是最好可能的。《Some Topics on Structural Invariants of Vertex-Disjoint Cycles in Graphs》的主要结果如下：**章引言部分，主要介绍常用的图论术语和基本引理，以及《Some Topics on Structural Invariants of Vertex-Disjoint Cycles in Graphs》的主要结果概述；第二章，确定了图上有指定个数点不交弦圈的邻域并条件，这个界是最好可能的；第三章基于构造性证明，给出了均衡二部图中点不交双弦圈的Dirac型*小度条件；第四章主要研究了图上有圈长限制以及指定顶点要求的两类2-因子问题，给出了Ore型界；第五章探讨了图上点不交三角形和四边形的填装问题，确定了在Ore型条件下图的*小阶数；第六章主要确定了一般图中包含指定个数独立偶长圈以及二分图中包含指定个数独立弦圈的边极值参数条件；第七章主要研究了有向图中包含独立圈的*小出度条件以及标准多重图中的Dirac型度条件；*后，第八章研究了*小度至少为4和5的某些特殊图上含小阶子图的点数极值条件。《Some Topics on Structural Invariants of Vertex-Disjoint Cycles in Graphs》详细介绍了上述问题的提出，发展过程以及完整的理论证明，并且提出了一些供进一步研究的问题。
目錄：
Contents
Preface
Notations
Chapter 1 Introduction and Main Results 1
1.1 Basic concepts and definitions 1
1.2 Invariants for 2-factors in graphs 3
1.3 Degree condition for 2-factors in bipartite graphs 8
1.4 Invariants for vertex-disjoint cycles in graphs 10
1.5 Invariants for vertex-disjoint cycles with constraints 15
1.5.1 Degree conditions for vertex-disjoint cycles containing prescribed elements 15
1.5.2 Degree conditions for vertex-disjoint cycles with length constraints in digraphs 20
1.5.3 Degree conditions for vertex-disjoint cycles with length constraints in tournaments 21
1.6 Outline the main results 23
Chapter 2 Neighborhood Unions for Disjoint Chorded Cycles in Graphs 26
2.1 Introduction 26
2.2 Basic induction 28
2.3 Proof of Theorem 2.4 28
Chapter 3 Vertex-Disjoint Double Chorded Cycles in Bipartite Graphs 38
3.1 Introduction 38
3.2 Lemmas 41
3.3 Proof of Theorem 3.5 58
Chapter 4 2-Factors with Specified Elements in Graphs 68
4.1 2-Factors with chorded quadrilaterals 68
4.1.1 Lemmas 69
4.1.2 Proof of Theorem 4.2 74
4.2 2-Factors Containing Specified Vertices in A Bipartite Graph 84
4.2.1 Lemmas 86
4.2.2 Proof of Theorem 4.6 91
4.2.3 Proof of Theorem 4.7 96
4.2.4 Discussion 99
Chapter 5 Packing Triangles and Quadrilaterals 100
5.1 Introduction and terminology 100
5.2 Lemmas 102
5.3 Proof of Theorem 5.3 108
Chapter 6 Extremal Function for Disjoint Chorded Cycles 123
6.1 Extremal function for disjoint cycles in graphs 123
6.2 Proof of Theorem 6.3 127
6.3 Basic Lemmas 131
6.4 Proof of Theorem 6.5 135
6.5 Proof of Theorem 6.9 143
6.6 Extremal function for disjoint cycles in bipartite graphs 151
6.7 Lemmas 152
6.8 Proof of Theorem 6.12 156
6.9 Proof of Theorem 6.13 157
6.10 Discussion 164
Chapter 7 Disjoint Cycles in Digraphs and Multigraphs 166
7.1 Disjoint cycles with di.erent lengths in digraphs 166
7.2 Disjoint quadrilaterals in digraphs 177
7.2.1 Introduction 177
7.2.2 Preliminary Lemmas 179
7.2.3 Proof of Theorem 7.2 181
Chapter 8 Vertex-Disjoint Subgraphs with Small Order and Small Minimum Degree 195
8.1 Disjoint F in K1;4-free graphs with minimum degree at least four 195
8.1.1 Preparation for the proof of the Theorem 8.4 198
8.1.2 Proof of the Theorem 8.4 211
8.2 Disjoint K.4 in claw-free graphs with minimum degree at least five 214
8.2.1 Definition of several graphs 215
8.2.2 Preparation for the proof of the Theorem 8.7 216
8.2.3 Proof of the Theorem 8.7 227
8.2.4 Discussion 227
References 229
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