## A Walk Through Combinatorics: An Introduction to Enumeration and Graph TheoryThis is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of exercises, ranging in difficulty from "routine" to "worthy of independent publication, " is included. In each section, there are also exercises that contain material not explicitly discussed in the text before, so as to provide instructors with extra choices if they want to shift the emphasis of their course. It goes without saying that the text covers the classic areas, i.e. combinatorial choice problems and graph theory. What is unusual, for an undergraduate textbook, is that the author has included a number of more elaborate concepts, such as Ramsey theory, the probabilistic method and -- probably the first of its kind -- pattern avoidance. While the reader can only skim the surface of these areas, the author believes that they are interesting enough to catch the attention of some students. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading. |

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### Contents

IV | 1 |

V | 3 |

VI | 10 |

VII | 11 |

VIII | 12 |

IX | 19 |

X | 25 |

XI | 26 |

LVII | 196 |

LVIII | 200 |

LX | 207 |

LXI | 214 |

LXII | 218 |

LXIII | 221 |

LXIV | 226 |

LXV | 229 |

XII | 28 |

XIII | 29 |

XIV | 37 |

XV | 40 |

XVI | 43 |

XVII | 47 |

XVIII | 51 |

XIX | 52 |

XX | 65 |

XXIV | 70 |

XXV | 73 |

XXVI | 75 |

XXVII | 78 |

XXVIII | 79 |

XXIX | 89 |

XXX | 91 |

XXXI | 94 |

XXXII | 100 |

XXXIII | 102 |

XXXIV | 103 |

XXXV | 109 |

XXXVI | 110 |

XXXVII | 116 |

XXXVIII | 120 |

XXXIX | 123 |

XLI | 131 |

XLIII | 134 |

XLIV | 138 |

XLV | 139 |

XLVI | 140 |

XLVII | 145 |

XLVIII | 160 |

XLIX | 168 |

L | 169 |

LI | 171 |

LII | 183 |

LIII | 184 |

LIV | 188 |

LV | 190 |

LVI | 193 |

LXVI | 230 |

LXVII | 239 |

LXVIII | 241 |

LXIX | 246 |

LXX | 252 |

LXXI | 254 |

LXXII | 258 |

LXXIII | 259 |

LXXIV | 260 |

LXXV | 265 |

LXXVII | 268 |

LXXVIII | 275 |

LXXIX | 278 |

LXXXI | 279 |

LXXXII | 283 |

LXXXIII | 289 |

LXXXIV | 292 |

LXXXV | 293 |

LXXXVI | 295 |

LXXXVII | 296 |

LXXXVIII | 301 |

LXXXIX | 313 |

XC | 324 |

XCI | 326 |

XCII | 327 |

XCIII | 339 |

XCIV | 343 |

XCV | 345 |

XCVI | 358 |

XCVII | 361 |

XCVIII | 362 |

XCIX | 369 |

C | 374 |

CI | 383 |

CII | 390 |

CIII | 392 |

CIV | 393 |

401 | |

403 | |

### Other editions - View all

A Walk Through Combinatorics: An Introduction to Enumeration and Graph ... MiklÃ³s BÃ³na Limited preview - 2006 |

A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory Mikl¢s B¢na Limited preview - 2006 |

A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory Miklós Bóna No preview available - 2006 |

### Common terms and phrases

2-color adjacency matrix antichain bijection bipartite graph block blue called Chapter choose claim coefficient combinatorics complete graph compute connected graph contain defined definition degree denote diagonal digits directed graph edges adjacent eigenvalues elements entries equal exactly Example exponential generating function Ferrers shape finite graph G Hamiltonian cycle implies induction hypothesis least left-hand side left-to-right minima Lemma length Let G matrix minimal Möbius function monochromatic multiset noncrossing partitions nonnegative integers Note number of edges number of vertices odd cycle odd number ordinary generating function pattern perfect matching permutation pigeon-hole principle planar graph players polyhedron polynomial poset positive integers previous exercise problem proof follows Ramsey theory real numbers recursive formula right-hand side rooted sequence shown in Figure shows simple graph smallest sortable spanning tree square stack statement is true subgraph teams Theorem tournament triangle vertex