6.2 The Addition and Multiplication Rules192
6.3 The Pigeonhole Principle199
Review Exercises204
7 Permutations and Combinations205
7.1 Permutations205
7.2 Combinations210
7.3 Elementary Probability216
7.4 Probability Theory224
7.5 Repetitions231
7.6 Derangements236
7.7 The Binomial Theorem239
Review Exercises245
8 Algorithms247
8.1 What Is an Algorithm?247
8.2 Complexity253
8.3 Searching and Sorting265
8.4 Enumeration of Permutations and Combinations276
Review Exercises280
9 Graphs281
9.1 A Gentle In troduction281
9.2 Definitions and Basic Properties288
9.3 Isomorphism296
Review Exercises 301
10 Paths and Circuits304
10.1 EulerianCircuits304
10.2 Hamiltonian Cycles311
10.3 The Adjacency Matrix319
10.4 Shortest Path Algorithms326
Review Exercises336
11 Applicationsof Paths and Circuits339
11.1 The Chinese Postman Problem339
11.2 Digraphs344
11.3 RNA Chains352
11.4 Tournaments356
11.5 Scheduling Problems361
Review Exercises367
12 Trees370
12.1 Trees and the irProperties370
12.2 Spanning Trees379
12.3 Minimum Spanning Tree Algorithms384
12.4 Acyclic Digraphs and Bellman's Algorithm393
12.5 Depth-FirstSearch398
12.6 The One-Way Street Problem403
Review Exercises409
13 Planar Graphs and Colorings411
13.1 Planar Graphs411
13.2 Coloring Grap

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