Preface |
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xi | |
Authors |
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xiii | |
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1 Introduction to Graph Models |
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1 | (58) |
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2 | (13) |
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1.2 Common Families of Graphs |
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15 | (7) |
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1.3 Graph Modeling Applications |
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22 | (7) |
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29 | (11) |
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1.5 Paths, Cycles, and Trees |
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40 | (9) |
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1.6 Vertex and Edge Attributes: More Applications |
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49 | (4) |
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1.7 Supplementary Exercises |
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53 | (1) |
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54 | (5) |
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2 Structure and Representation |
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59 | (62) |
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60 | (8) |
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2.2 Automorphisms and Symmetry |
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68 | (6) |
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74 | (9) |
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2.4 Some Graph Operations |
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83 | (10) |
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2.5 Tests for Non-Isomorphism |
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93 | (7) |
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2.6 Matrix Representations |
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100 | (5) |
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2.7 More Graph Operations |
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105 | (8) |
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2.8 Supplementary Exercises |
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113 | (2) |
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115 | (6) |
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121 | (52) |
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3.1 Characterizations and Properties of Trees |
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122 | (8) |
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3.2 Rooted Trees, Ordered Trees, and Binary Trees |
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130 | (8) |
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3.3 Binary-Tree Traversal |
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138 | (5) |
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143 | (5) |
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3.5 Huffman Trees and Optimal Prefix Codes |
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148 | (4) |
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152 | (5) |
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3.7 Counting Labeled Trees: Prufer Encoding |
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157 | (6) |
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3.8 Counting Binary Trees: Catalan Recursion |
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163 | (2) |
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3.9 Supplementary Exercises |
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165 | (3) |
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168 | (5) |
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173 | (56) |
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174 | (7) |
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4.2 Depth-First and Breadth-First Search |
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181 | (5) |
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4.3 Minimum Spanning Trees and Shortest Paths |
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186 | (7) |
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4.4 Applications of Depth-First Search |
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193 | (8) |
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4.5 Cycles, Edge-Cuts, and Spanning Trees |
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201 | (6) |
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4.6 Graphs and Vector Spaces |
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207 | (11) |
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4.7 Matroids and the Greedy Algorithm |
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218 | (5) |
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4.8 Supplementary Exercises |
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223 | (1) |
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224 | (5) |
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229 | (30) |
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5.1 Vertex- and Edge-Connectivity |
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230 | (5) |
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5.2 Constructing Reliable Networks |
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235 | (8) |
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5.3 Max-Min Duality and Menger's Theorems |
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243 | (9) |
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252 | (4) |
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5.5 Supplementary Exercises |
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256 | (1) |
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257 | (2) |
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6 Optimal Graph Traversals |
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259 | (38) |
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6.1 Eulerian Trails and Tours' |
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260 | (4) |
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6.2 DeBruijn Sequences and Postman Problems |
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264 | (15) |
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6.3 Hamiltonian Paths and Cycles |
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279 | (5) |
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6.4 Gray Codes and Traveling Salesman Problems |
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284 | (10) |
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6.5 Supplementary Exercises |
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294 | (1) |
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295 | (2) |
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7 Planarity and Kuratowski's Theorem |
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297 | (54) |
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7.1 Planar Drawings and Some Basic Surfaces |
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298 | (7) |
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7.2 Subdivision and Homeomorphism |
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305 | (4) |
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7.3 Extending Planar Drawings |
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309 | (7) |
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316 | (8) |
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7.5 Algebraic Tests for Planarity |
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324 | (13) |
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337 | (3) |
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7.7 Crossing Numbers and Thickness |
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340 | (5) |
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7.8 Supplementary Exercises |
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345 | (2) |
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347 | (4) |
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351 | (48) |
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352 | (15) |
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367 | (7) |
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374 | (14) |
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388 | (5) |
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8.5 Supplementary Exercises |
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393 | (2) |
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395 | (4) |
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399 | (42) |
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9.1 Directed Paths and Mutual Reachability |
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400 | (11) |
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9.2 Digraphs as Models for Relations |
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411 | (6) |
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417 | (5) |
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422 | (7) |
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9.5 Finding the Strong Components of a Digraph |
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429 | (6) |
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9.6 Supplementary Exercises |
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435 | (1) |
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436 | (5) |
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10 Network Flows and Applications |
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441 | (46) |
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10.1 Flows and Cuts in Networks |
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442 | (8) |
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10.2 Solving the Maximum-Flow Problem |
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450 | (10) |
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10.3 Flows and Connectivity |
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460 | (9) |
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10.4 Matchings, Transversals, and Vertex Covers |
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469 | (13) |
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10.5 Supplementary Exercises |
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482 | (1) |
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483 | (4) |
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11 Graph Colorings and Symmetry |
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487 | (14) |
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11.1 Automorphisms of Simple Graphs |
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488 | (5) |
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11.2 Equivalence Classes of Colorings |
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493 | (6) |
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11.3 Supplementary Exercises |
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499 | (1) |
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500 | (1) |
A Appendix |
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501 | (14) |
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501 | (1) |
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A.2 Relations and Functions |
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502 | (3) |
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A.3 Some Basic Combinatorics |
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505 | (1) |
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506 | (5) |
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A.5 Algorithmic Complexity |
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511 | (3) |
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A.6 Supplementary Reading |
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514 | (1) |
B Bibliography |
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515 | (8) |
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515 | (2) |
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517 | (6) |
Solutions and Hints |
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523 | (40) |
Index of Applications |
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563 | (2) |
Index Of Algorithms |
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565 | (2) |
General Index |
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567 | |