Preface Chapter 1 Fundamental Concepts 1.1 What Is a Graph? The Definition Graphs as Models Matrices and Ismorphism Decomposition and Special Graphs Exercises 1.2 Paths,Cycles,and Trails Connection in Graphs Bipartite Graphs Exercises 1.3 Vertex Degrees and Counting Counting and Bijections Extremal Problems Graphic Sequences Excercises 1.4 Directed Graphs Definitions and Examples Vertex Degrees Eulerian Digraphs Orientations and Tournaments Exercises Chapter 2 Trees and Distance 2.1 Basic Properties Properties of Trees Distance in Trees and Graphs Disjoint Spanning Trees(optional) Exercises 2.2 Spanning Trees and Enumeration Enumeration of Trees Spanning Trees in Graphs Decomposition and Graceful Labelings Branchings and Eulerian Digraphs(optional) 2.3 Optimization and Trees Minimum Spanning Tree Shortese Paths Trees in Computer Science(optional) Exercises Chapter 3 Matchings and Factors 3.1 Matchings and Covers Maximum Matchings Hall's Matching Condition Min-Max Theorems Independent Sets and Covers Dominating Sets(optional) Exercises 3.2 Algorithms and Applications Maximum Bipartite Matching Weighted Bipartite Matching Stable Matchings(optional) Faster Bipartite Matching(optional) Exercises 3.3 Matchings in General Graphs Tutt's 1-factor Hteorem f-factors of Graphs(optional) Edmonds'Blossom Algorithm(optional) Exercises ……