Combinatorics and Graph Theory
by Harris, John M.; Hirst, Jeffry L.; Mossinghoff, Michael J.Edition: 2nd
Format: Hardcover
Pub. Date: 2008-09-01
Publisher(s): Springer Verlag
Other versions by this Author
List Price: $63.33
Buy New
Usually Ships in 24-48 Hours
$60.31
Rent Textbook
Select for Price
Rent Digital
$39.00*
Used Textbook
We're Sorry
Sold Out
How Marketplace Works:
- This item is offered by an independent seller and not shipped from our warehouse
- Item details like edition and cover design may differ from our description; see seller's comments before ordering.
- Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
- Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
- Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.
Summary
"This book covers a wide variety of topics in combinatorics and graph theory. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics. In addition, recent results appear in the text, illustrating the fact that mathematics is a living discipline."--BOOK JACKET.
Table of Contents
| Preface to the Second Edition | p. vii |
| Preface to the First Edition | p. ix |
| Graph Theory | p. 1 |
| Introductory Concepts | p. 2 |
| Graphs and Their Relatives | p. 2 |
| The Basics | p. 5 |
| Special Types of Graphs | p. 10 |
| Distance in Graphs | p. 17 |
| Definitions and a Few Properties | p. 18 |
| Graphs and Matrices | p. 21 |
| Graph Models and Distance | p. 26 |
| Trees | p. 30 |
| Definitions and Examples | p. 31 |
| Properties of Trees | p. 34 |
| Spanning Trees | p. 38 |
| Counting Trees | p. 43 |
| Trails, Circuits, Paths, and Cycles | p. 51 |
| The Bridges of Konigsberg | p. 52 |
| Eulerian Trails and Circuits | p. 55 |
| Hamiltonian Paths and Cycles | p. 60 |
| Three Open Problems | p. 67 |
| Planarity | p. 73 |
| Definitions and Examples | p. 74 |
| Euler's Formula and Beyond | p. 78 |
| Regular Polyhedra | p. 80 |
| Kuratowski's Theorem | p. 83 |
| Colorings | p. 85 |
| Definitions | p. 86 |
| Bounds on Chromatic Number | p. 88 |
| The Four Color Problem | p. 93 |
| Chromatic Polynomials | p. 97 |
| Matchings | p. 101 |
| Definitions | p. 102 |
| Hall's Theorem and SDRs | p. 104 |
| The Konig-Egervary Theorem | p. 109 |
| Perfect Matchings | p. 111 |
| Ramsey Theory | p. 116 |
| Classical Ramsey Numbers | p. 116 |
| Exact Ramsey Numbers and Bounds | p. 118 |
| Graph Ramsey Theory | p. 124 |
| References | p. 126 |
| Combinatorics | p. 129 |
| Some Essential Problems | p. 130 |
| Binomial Coefficients | p. 137 |
| Multinomial Coefficients | p. 144 |
| The Pigeonhole Principle | p. 150 |
| The Principle of Inclusion and Exclusion | p. 156 |
| Generating Functions | p. 164 |
| Double Decks | p. 166 |
| Counting with Repetition | p. 168 |
| Changing Money | p. 171 |
| Fibonacci Numbers | p. 177 |
| Recurrence Relations | p. 181 |
| Catalan Numbers | p. 185 |
| Polya's Theory of Counting | p. 190 |
| Permutation Groups | p. 191 |
| Burnside's Lemma | p. 196 |
| The Cycle Index | p. 200 |
| Polya's Enumeration Formula | p. 202 |
| de Bruijn's Generalization | p. 209 |
| More Numbers | p. 217 |
| Partitions | p. 218 |
| Stirling Cycle Numbers | p. 227 |
| Stirling Set Numbers | p. 231 |
| Bell Numbers | p. 237 |
| Eulerian Numbers | p. 242 |
| Stable Marriage | p. 248 |
| The Gale-Shapley Algorithm | p. 250 |
| Variations on Stable Marriage | p. 250 |
| Combinatorial Geometry | p. 264 |
| Sylvester's Problem | p. 265 |
| Convex Polygons | p. 270 |
| References | p. 277 |
| Infinite Combinatorics and Graphs | p. 281 |
| Pigeons and Trees | p. 282 |
| Ramsey Revisited | p. 285 |
| ZFC | p. 290 |
| Language and Logical Axioms | p. 290 |
| Proper Axioms | p. 292 |
| Axiom of Choice | p. 297 |
| The Return of der Konig | p. 301 |
| Ordinals, Cardinals, and Many Pigeons | p. 304 |
| Cardinality | p. 304 |
| Ordinals and Cardinals | p. 308 |
| Pigeons Finished Off | p. 312 |
| Incompleteness and Cardinals | p. 318 |
| Godel's Theorems for PA and ZFC | p. 318 |
| Inaccessible Cardinals | p. 320 |
| A Small Collage of Large Cardinals | p. 322 |
| Weakly Compact Cardinals | p. 324 |
| Infinite Marriage Problems | p. 327 |
| Hall and Hall | p. 328 |
| Countably Many Men | p. 330 |
| Uncountably Many Men | p. 336 |
| Espousable Cardinals | p. 340 |
| Perfect Matchings | p. 343 |
| Finite Combinatorics with Infinite Consequences | p. 344 |
| k-critical Linear Orderings | p. 347 |
| Points of Departure | p. 348 |
| References | p. 352 |
| References | p. 355 |
| Index | p. 369 |
| Table of Contents provided by Ingram. All Rights Reserved. |
An electronic version of this book is available through VitalSource.
This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.
By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.
Digital License
You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.
More details can be found here.
A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.
Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.
Please view the compatibility matrix prior to purchase.