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E-raamat: Chromatic Graph Theory

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(Western Michigan University, Kalamazoo, Michigan, USA),
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With Chromatic Graph Theory, Second Edition, the authors present various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. Readers will see that the authors accomplished the primary goal of this textbook, which is to introduce graph theory with a coloring theme and to look at graph colorings in various ways.

The textbook also covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings.

Features of the Second Edition:











The book can be used for a first course in graph theory as well as a graduate course





The primary topic in the book is graph coloring





The book begins with an introduction to graph theory so assumes no previous course





The authors are the most widely-published team on graph theory





Many new examples and exercises enhance the new edition
Preface To The Second Edition xi
List of Symbols
xix
0 The Origin of Graph Colorings
1(26)
1 Introduction to Graphs
27(26)
1.1 Fundamental Terminology
27(3)
1.2 Connected Graphs
30(4)
1.3 Distance in Graphs
34(3)
1.4 Isomorphic Graphs
37(2)
1.5 Common Graphs and Graph Operations
39(6)
1.6 Multigraphs and Digraphs
45(8)
Exercises for
Chapter 1
48(5)
2 Trees and Connectivity
53(18)
2.1 Cut-Vertices, Bridges, and Blocks
53(3)
2.2 Trees
56(4)
2.3 Connectivity and Edge-Connectivity
60(3)
2.4 Menger's Theorem
63(8)
Exercises for
Chapter 2
67(4)
3 Eulerian and Hamiltonian Graphs
71(20)
3.1 Eulerian Graphs
3.2 De Bruijn Digraphs
76(3)
3.3 Hamiltonian Graphs
79(12)
Exercises for
Chapter 3
87(4)
4 Matchings and Factorization
91(18)
4.1 Matchings and Independence
91(8)
4.2 Factorization and Decomposition
99(10)
Exercises for
Chapter 4
105(4)
5 Graph Embeddings
109(38)
5.1 Planar Graphs and the Euler Identity
109(9)
5.2 Hamiltonian Planar Graphs
118(2)
5.3 Planarity versus Nonplanarity
120(9)
5.4 Outerplanar Graphs
129(2)
5.5 Embedding Graphs on Surfaces
131(8)
5.6 The Graph Minor Theorem
139(8)
Exercises for
Chapter 5
141(6)
6 Introduction to Vertex Colorings
147(28)
6.1 The Chromatic Number of a Graph
147(6)
6.2 Applications of Colorings
153(7)
6.3 Perfect Graphs
160(15)
Exercises for
Chapter 6
170(5)
7 Bounds for the Chromatic Number
175(30)
7.1 Color-Critical Graphs
175(4)
7.2 Upper Bounds and Greedy Colorings
179(10)
7.3 Upper Bounds and Oriented Graphs
189(6)
7.4 The Chromatic Number of Cartesian Products
195(10)
Exercises for
Chapter 7
200(5)
8 Coloring Graphs on Surfaces
205(18)
8.1 The Four Color Problem
205(3)
8.2 The Conjectures of Hajos and Hadwiger
208(3)
8.3 Chromatic Polynomials
211(6)
8.4 The Heawood Map-Coloring Problem
217(6)
Exercises for
Chapter 8
220(3)
9 Restricted Vertex Colorings
223(26)
9.1 Uniquely Colorable Graphs
223(7)
9.2 List Colorings
230(10)
9.3 Precoloring Extensions of Graphs
240(9)
Exercises for
Chapter 9
245(4)
10 Edge Colorings
249(40)
10.1 The Chromatic Index and Vizing's Theorem
249(6)
10.2 Class One and Class Two Graphs
255(7)
10.3 Tait Colorings
262(7)
10.4 Nowhere-Zero Flows
269(10)
10.5 List Edge Colorings
279(3)
10.6 Total Colorings of Graphs
282(7)
Exercises for
Chapter 10
284(5)
11 Ramsey Theory
289(26)
11.1 Ramsey Numbers
289(8)
11.2 Bipartite Ramsey Numbers
297(8)
11.3 s-Bipartite Ramsey Numbers
305(10)
Exercises for
Chapter 11
311(4)
12 Monochromatic Ramsey Theory
315(28)
12.1 Monochromatic Ramsey Numbers
315(4)
12.2 Monochromatic-Bichromatic Ramsey Numbers
319(3)
12.3 Proper Ramsey Numbers
322(5)
12.4 Rainbow Ramsey Numbers
327(6)
12.5 Gallai-Ramsey Numbers
333(10)
Exercises for
Chapter 12
340(3)
13 Color Connection
343(32)
13.1 Rainbow Connection
344(8)
13.2 Proper Connection
352(11)
13.3 Rainbow Disconnection
363(12)
Exercises for
Chapter 13
372(3)
14 Distance and Colorings
375(30)
14.1 T-Colorings
376(5)
14.2 L(2, l)-Colorings
381(6)
14.3 Radio Colorings
387(7)
14.4 Hamiltonian Colorings
394(11)
Exercises for
Chapter 14
402(3)
15 Domination and Colorings
405(18)
15.1 Domination Parameters
405(3)
15.2 Stratified Domination
408(6)
15.3 Domination Based on AT3-Colorings
414(4)
15.4 Stratified Domination by Multiple Graphs
418(5)
Exercises for
Chapter 15
420(3)
16 Induced Colorings
423(38)
16.1 Majestic Colorings
423(9)
16.2 Royal and Regal Colorings
432(16)
16.3 Rainbow Mean Colorings
448(13)
Exercises for
Chapter 16
456(5)
17 The Four Color Theorem Revisited
461(14)
17.1 Zonal Labelings of Planar Graphs
461(3)
17.2 Zonal Labelings and Edge Colorings
464(11)
Exercises for
Chapter 17
472(3)
Bibliography 475(13)
Index (Names and Mathematical Terms) 488
Gary Chartrand is a professor emeritus of mathematics at Western Michigan University.

Ping Zhang is a professor of mathematics at Western Michigan University.

The two have authored or co-authored many textbooks in mathematics and numerous research articles in graph theory. The authors publish several books on graph theory, including the best-selling Graphs and Diagraphs, Sixth Edition, CRC Press, the most widely-used introductory text for course in graph theory.
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