Pearls in Graph Theory: A Comprehensive Introduction Book

	Foreword to the Revised Edition	vii
	Foreword	ix
Chapter 1.	Basic Graph Theory
1.1	Graphs and Degrees of Vertices	1
1.2	Subgraphs, Isomorphic Graphs	13
1.3	Trees	17
Chapter 2.	Colorings of Graphs
2.1	Vertex Colorings	23
2.2	Edge Colorings	31
2.3	Decompositions and Hamilton Cycles	35
2.4	More Decomposition	43
Chapter 3.	Circuits and Cycles
3.1	Eulerian Circuits	49
3.2	The Oberwolfach Problem	58
3.3	Infinite Lattice Graphs	65
Chapter 4.	Extremal Problems
4.1	A Theorem of Turan	70
4.2	Cages	77
4.3	Ramsey Theory	81
Chapter 5.	Counting
5.1	Counting 1-Factors	87
5.2	Cayley's Spanning Tree Formula	94
5.3	More Spanning Trees	100
Chapter 6.	Labeling Graphs
6.1	Magic Graphs and Graceful Trees	104
6.2	Conservative Graphs	114
Chapter 7.	Applications and Algorithms
7.1	Spanning Tree Algorithms	125
7.2	Matchings in Graphs, Scheduling Problems	133
7.3	Binary Trees and Prefix Codes	140
Chapter 8.	Drawings of Graphs
8.1	Planar Graphs	149
8.2	The Four Color Theorem	156
8.3	The Five Color Theorem	164
8.4	Graphs and Geometry	168
Chapter 9.	Measurements of Closeness to Planarity
9.1	Crossing Number	179
9.2	Thickness and Splitting Number	190
9.3	Heawood's Empire Problem	197
Chapter 10.	Graphs on Surfaces
10.1	Rotations of Graphs	208
10.2	Planar Graphs Revisited	217
10.3	The Genus of a Graph	225
	References	241
	Index	245