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. |