●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.
Chapter 3 Vertex-Disjoint Double Chorded Cycles in Bipartite Graphs
3.1 Introduction
3.2 Lemmas
3.3 Proof of Theorem 3.
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.
4.2 2-Factors Containing Specified Vertices in A Bipartite Graph
4.2.1 Lemmas
4.2.2 Proof of Theorem 4.
4.2.3 Proof of Theorem 4.
4.2.4 Discussion
Chapter 5 Packing Triangles and Quadrilaterals
5.1 Introduction and terminology
5.2 Lemmas
5.3 Proof of Theorem 5.
Chapter 6 Extremal Function for Disjoint Chorded Cycles
6.1 Extremal function for disjoint cycles in graphs
6.2 Proof of Theorem 6.
6.3 Basic Lemmas
6.4 Proof of Theorem 6.
6.5 Proof of Theorem 6.
6.6 Extremal function for disjoint cycles in bipartite graphs
6.7 Lemmas
6.8 Proof of Theorem 6.
6.9 Proof of Theorem 6.
6.10 Discussion
Chapter 7 Disjoint Cycles in Digraphs and ltigraphs
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.
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.
8.1.2 Proof of the Theorem 8.
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.
8.2.3 Proof of the Theorem 8.
8.2.4 Discussion
References

圖的點不交圈問題是有名的哈密爾頓圈及2-因子問題的推廣，具有重要的理論價值和實際應用價值，是圖論研究的核心問題之一。本書主要研究了圖上有條件的點不交圈結構參數，主要包括Dirac型最小度參數、極值參數以及鄰域並參數，本書得到的這些參數大多是優選可能的。本書的主要結果如下：第一章引言部分，主要介紹常用的圖論術語和基本引理，以及本書的主要結果概述；第二章，確定了圖上有指定個數點不交弦圈的鄰域並條件，這個界是優選可能的；第三章基於構造性證明，給出了均衡二部圖中點不交雙弦圈的Dirac型最小度條件；第四章主要研究了圖上有圈長以及指定頂點要求的兩類2-因子問題，給出了Ore型界；第五章探討了圖上點不交三角形和四邊形的填裝問題，確定了在Ore型條件下圖的最小階數；第六章主要確定了一般圖中包含指定個數獨立偶長圈以及二分圖中包含指定個數獨立弦圈的邊極值參數條件；第七章主要研究了有向圖中包含獨立圈的最小出度等