Note: Supplemental materials are not guaranteed with Rental or Used book purchases.
Purchase Benefits
What is included with this book?
Foreword | p. xv |
Preface | p. xvii |
Introduction | p. 1 |
Graph theory | p. 1 |
Graphs in the plane | p. 10 |
Surfaces | p. 12 |
Graphs on surfaces | p. 14 |
Embedding graphs on surfaces | p. 18 |
Introduction | p. 18 |
Graphs and surfaces | p. 19 |
Embeddings | p. 20 |
Rotation systems | p. 23 |
Covering spaces and voltage graphs | p. 26 |
Enumeration | p. 29 |
Algorithms | p. 30 |
Graph minors | p. 31 |
Maximum genus | p. 34 |
Introduction | p. 34 |
Characterizations and complexity | p. 36 |
Kuratowski-type theorems | p. 38 |
Upper-embeddability | p. 39 |
Lower bounds | p. 40 |
Distribution of embeddings | p. 45 |
Introduction | p. 45 |
Enumerating embeddings by surface type | p. 48 |
Total embedding distributions | p. 51 |
Congruence classes | p. 53 |
The unimodality problem | p. 55 |
Average genus | p. 56 |
Stratification of embeddings | p. 59 |
Algorithms and obstructions for embeddings | p. 62 |
Introduction | p. 62 |
Planarity | p. 64 |
Outerplanarity and face covers | p. 66 |
Disc embeddings and the 2-path problem | p. 68 |
Graph minors and obstructions | p. 69 |
Algorithms for embeddability in general surfaces | p. 73 |
Computing the genus | p. 75 |
Graph minors: generalizing Kuratowski's theorem | p. 81 |
Introduction | p. 81 |
Graph decompositions | p. 84 |
Linked decompositions | p. 88 |
Graphs with bounded tree-width | p. 94 |
Finding large grids | p. 99 |
Embedding large grids | p. 107 |
Colouring graphs on surfaces | p. 111 |
Introduction | p. 111 |
High-end colouring | p. 113 |
A transition from high-end to low-end colouring | p. 116 |
Colouring graphs with few colours | p. 119 |
Girth and chromatic number | p. 124 |
List-colouring graphs | p. 125 |
More colouring extensions | p. 127 |
An open problem | p. 129 |
Crossing numbers | p. 133 |
Introduction | p. 133 |
What is the crossing number? | p. 135 |
General bounds | p. 137 |
Applications to geometry | p. 139 |
Crossing-critical graphs | p. 139 |
Other families of graphs | p. 143 |
Algorithmic questions | p. 144 |
Drawings in other surfaces | p. 146 |
Conclusion | p. 147 |
Representing graphs and maps | p. 151 |
Introduction | p. 151 |
Representations of graphs | p. 152 |
Energy and optimal representations | p. 155 |
Representations of maps | p. 163 |
Representations of maps in the plane | p. 170 |
Representations of incidence geometries and related topics | p. 174 |
Enumerating coverings | p. 181 |
Introduction | p. 181 |
Graph coverings | p. 183 |
Regular coverings | p. 185 |
Surface branched coverings | p. 190 |
Regular surface branched coverings | p. 193 |
Distribution of surface branched coverings | p. 195 |
Further remarks | p. 196 |
Symmetric maps | p. 199 |
Introduction | p. 199 |
Representing maps algebraically | p. 200 |
Regular maps | p. 205 |
Cayley maps | p. 210 |
Regular Cayley maps | p. 212 |
Edge-transitive maps | p. 218 |
Maps and mathematics | p. 221 |
The genus of a group | p. 225 |
Introduction | p. 225 |
Symmetric embeddings and groups acting on surfaces | p. 226 |
Quotient embeddings and voltage graphs | p. 228 |
Inequalities | p. 232 |
Groups of low genus | p. 235 |
Genera of families of groups | p. 239 |
Embeddings and geometries | p. 245 |
Introduction | p. 245 |
Surface models | p. 248 |
Projective geometries | p. 250 |
Affine geometries | p. 253 |
3-configurations | p. 256 |
Partial geometries | p. 260 |
Regular embeddings for PG(2,n) | p. 264 |
Problems | p. 265 |
Embeddings and designs | p. 268 |
Introduction | p. 268 |
Steiner triple systems and triangulations | p. 270 |
Recursive constructions | p. 273 |
Small systems | p. 278 |
Cyclic embeddings | p. 280 |
Concluding remarks | p. 284 |
Infinite graphs and planar maps | p. 289 |
Introduction | p. 289 |
Ends | p. 290 |
Automorphisms | p. 293 |
Connectivities | p. 295 |
Growth | p. 300 |
Infinite planar graphs and maps | p. 303 |
Open problems | p. 313 |
Introduction | p. 313 |
Drawings and crossings | p. 314 |
Genus and obstructions | p. 317 |
Cycles and factors | p. 320 |
Colourings and flows | p. 322 |
Local planarity | p. 324 |
Thickness, book embeddings and-covering graphs | p. 325 |
Geometrical topics | p. 328 |
Algorithms | p. 330 |
Infinite graphs | p. 332 |
Notes on contributors | p. 337 |
Index | p. 341 |
Table of Contents provided by Ingram. All Rights Reserved. |
The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.