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| Gary Chartrand 世界顶尖的图论专家。密歇根州立大学博士，现为西密歇根大学教授。他在图论领域发表了数量众多的优秀论文，总数排名世界第4位。合作者包括Erdos和Frank Harary等名家。. Ping Zhang密歇根州立大学博士，现为西密歇根大学教授。与Gary Chartrand合著过多本畅销教材。... .. << 查看详细 |
| 1. introduction . 1.1. graphs and graph models 1 1.2. connected graphs 9 1.3. common classes of graphs 19 1.4. multigraphs and digraphs 26 2. degrees 2.1. the degree of a vertex 31 2.2. regular graphs 38 2.3. degree sequences 43 2.4. excursion:graphs and matrices 48 2.5. exploration:irregular graphs 50 3. isomorphic graphs 3.1. the definiition of isomorphism 55 3.2. isomorphism as a relation 63 3.3. excursion:graphs and groups 66 3.4. excursion:reconstruction and solvability 76 4. trees 4.1. bridges 85 4.2. trees 87 4.3. the minimum spanning tree problem 94 .4.4. excursion:the number of spanning trees 101 5. connectivity 5.1. cut-vertices 107 5.2. blocks 111 5.3. connectivity 115 5.4. menger's theorem 124 5.5. exploration:geodetic sets 130 6. traversability 6.1. eulerian graphs 133 6.2. hamiltonian graphs 140 6.3. exploration:hamiltonian walks and numbers 152 6.4. excursion:the early books of graph theory 156 7. digraphs 7.1. strong digraphs 161 7.2. tournaments 169 7.3. excursion:decision-making 176 7.4. exploration:wine bottle problems 180 8. matchings and factorization 8.1. matchings 183 8.2. factorization .. 194 8.3. decompositions and graceful labelings 209 8.4. excursion:instant insanity 214 8.5. excursion:the petersen graph 219 8.6. exploration:γ-labelings of graphs 224 9. planarity 9.1. planar graphs 227 9.2. embedding graphs on surfaces 241 9.3. excursion:graph minors 249 9.4. exploration:embedding graphs in graphs 253 10. coloring 10.1. the four color problem 259 10.2. vertex coloring 267 10.3. edge coloring 280 10.4. excursion:the heawood map coloring theorem 288 10.5. exploration:local coloring 293 11. ramsey numbers 11.1. the ramsey number of graphs 297 11.2. turan's theorem 307 11.3. exploration:rainbow ramsey numbers 314 11.4. excursion:erdos numbers 321 12. distance 12.1. the center of a graph 327 12.2. distant vertices 333 12.3. excursion:locating numbers 341 12.4. excursion:detour and directed distance 346 12.5. exploration:channel assignment 351 12.6. exploration:distance between graphs 357 13. domination 13.1. the domination number of a graph 361 13.2. exploration:stratification 372 13.3. exploration:lights out 377 13.4. excursion:and still it grows more colorful 381 solutions and hints for odd-numbered exercises 383 references 411 index of names 423 index of mathematical terms 426 list of symbols ... 433 |
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