Graphs & Digraphs, Fifth Edition

Written for advanced undergraduate and beginning graduate students, the fifth edition of this best-selling book provides a wide range of new examples along with historical discussions of mathematicians, problems, and conjectures. It features new and expanded coverage of such topics as toughness, graph minors, perfect graphs, list colorings, nowhere zero flows, list edge colorings, the road coloring problem, and the rainbow number of a graph. Additional applications, exercises, and examples illustrate the concepts and theorems. A solutions manual is available for qualifying instructors.

ISBN 1439826277   DEWEY edition DC22 ISBN13 9781439826270 (What's this?)   Pages 598 Publisher Taylor & Francis Ltd   Weight (grammes) 975 Imprint Chapman & Hall/CRC   Previous ISBN 9781584883906 Format Hardback   Height (mm) 235 Publication date 18 Oct 2010   Width (mm) 156 DEWEY 511.5   Academic level Undergraduate

		Preface to the Fifth Edition
1		Introduction to Graphs		1
1.1		Graphs and Subgraphs		1
1.2		Degree Sequences		22
1.3		Connected Graphs and Distance		30
1.4		Multigraphs and Digraphs		45
2		Trees and Connectivity		55
2.1		Nonseparable Graphs		55
2.2		Trees		61
2.3		Spanning Trees		69
2.4		Connectivity and Edge-Connectivity		89
2.5		Menger's Theorem		97
3		Eulerian and Hamiltonian Graphs		107
3.1		Eulerian Graphs		107
3.2		Hamiltonian Graphs		115
3.3		Powers of Graphs and Line Graphs		137
4		Digraphs		149
4.1		Strong Digraphs		149
4.2		Tournaments		156
4.3		Flows in Networks		171
5		Graphs: History and Symmetry		195
5.1		Some Historical Figures of Graph Theory		195
5.2		The Automorphism Group of a Graph		201
5.3		Cayley Color Graphs		206
5.4		The Reconstruction Problem		212
6		Planar Graphs		221
6.1		The Euler Identity		221
6.2		Planarity versus Nonplanarity		235
		More...

As with the earlier editions, the current text emphasizes clear exposition, well-written proofs, and many original and innovative exercises of varying difficulty and challenge. ! The fifth edition continues and extends these fine traditions. --Arthur T. White, Zentralblatt MATH 1211 Now in its fifth edition, its success as a textbook is indicative of its quality and its clarity of presentation ! The authors also describe the fascinating history behind some of the key problems in graph theory, and, to a lesser extent, their applications. This book describes the key concepts you need to get started in graph theory ! . It provides all you might need to know about graph embeddings and graph colorings. Moreover, it analyzes many other topics that more general discrete mathematics monographs do not always cover, such as network flows, minimum cuts, matchings, factorization, decomposition, and even extremal graph theory ! this thorough textbook includes hundreds of exercises at the end of each section. Hints and solutions for odd-numbered exercises are included in the appendix, making it especially suitable for self-learning. --Fernando Berzal, Computing Reviews, September 2011 Praise for the Fourth Edition: ! a popular point of entry to the field ! has evolved with the field from a purely mathematical treatment to one that also addresses the needs of computer scientists. --L'Enseignement Mathematique ! emphasizes clear exposition, well-written proofs, and many original and innovative exercises of varying difficulty and challenge ! For 25 years, Graphs & Digraphs, in its various editions, has served as an exemplary introduction to the emerging mathematical disciplines of graph theories, for advanced undergraduate and graduate students. It has also served established graph theorists, combinatorialists, and other discrete mathematicians, as well as computer scientists and chemists, as a useful reference work. The fourth edition continues these fine traditions. --Zentralblatt MATH

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