## Graph TheoryThe third edition of this standard textbook of modern graph theory has been carefully revised, updated, and substantially extended. Covering all its major recent developments it can be used both as a reliable textbook for an introductory course and as a graduate text: on each topic it covers all the basic material in full detail, and adds one or two deeper results (again with detailed proofs) to illustrate the more advanced methods of that field. From the reviews of the first two editions (1997, 2000):"This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory." Acta Scientiarum Mathematiciarum"The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theory." Bulletin of the Institute of Combinatorics and its Applications"A highlight of the book is what is by far the best account in print of the Seymour-Robertson theory of graph minors." Mathematika". . . like listening to someone explain mathematics." Bulletin of the AMS |

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### Contents

I | 1 |

II | 2 |

III | 5 |

IV | 6 |

V | 10 |

VI | 13 |

VII | 17 |

VIII | 18 |

LIV | 160 |

LV | 161 |

LVI | 163 |

LVII | 164 |

LVIII | 169 |

LIX | 172 |

LX | 175 |

LXI | 183 |

IX | 21 |

X | 23 |

XI | 28 |

XII | 30 |

XIII | 32 |

XIV | 33 |

XV | 34 |

XVI | 39 |

XVII | 44 |

XVIII | 46 |

XIX | 49 |

XX | 51 |

XXI | 53 |

XXII | 55 |

XXIV | 57 |

XXV | 62 |

XXVI | 67 |

XXVII | 69 |

XXVIII | 78 |

XXIX | 80 |

XXX | 83 |

XXXI | 84 |

XXXII | 86 |

XXXIII | 92 |

XXXIV | 96 |

XXXV | 101 |

XXXVI | 103 |

XXXVII | 106 |

XXXVIII | 109 |

XXXIX | 111 |

XL | 112 |

XLI | 114 |

XLII | 119 |

XLIII | 121 |

XLIV | 126 |

XLV | 133 |

XLVI | 136 |

XLVII | 139 |

XLVIII | 140 |

XLIX | 141 |

L | 144 |

LI | 149 |

LII | 152 |

LIII | 156 |

LXII | 189 |

LXIII | 192 |

LXIV | 195 |

LXV | 196 |

LXVI | 204 |

LXVII | 212 |

LXVIII | 216 |

LXIX | 226 |

LXX | 237 |

LXXI | 244 |

LXXII | 251 |

LXXIII | 252 |

LXXIV | 255 |

LXXV | 258 |

LXXVI | 268 |

LXXVII | 271 |

LXXVIII | 272 |

LXXIX | 275 |

LXXXI | 278 |

LXXXII | 281 |

LXXXIII | 289 |

LXXXIV | 290 |

LXXXV | 293 |

LXXXVI | 294 |

LXXXVII | 299 |

LXXXVIII | 302 |

LXXXIX | 306 |

XC | 312 |

XCI | 313 |

XCII | 315 |

XCIII | 316 |

XCIV | 317 |

XCV | 319 |

XCVI | 327 |

XCVII | 341 |

XCVIII | 350 |

XCIX | 354 |

C | 357 |

CI | 361 |

CII | 369 |

393 | |

409 | |

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### Common terms and phrases

1-factor 3-connected A-B paths adjacent Algebraic assertion average degree bipartite graph Chapter choose chromatic number circle combinatorial component of G connected graph consider construct contradiction Corollary countable graph cycle in G cycle space define definition deleting denote disjoint e-regular edge of G edge set edge-disjoint embedding Erdos Exercise exists face formally four colour theorem function G contains graph G graph minor graph theory grid Hamilton cycle hence homeomorphism implies induced subgraph infinite graphs integer isomorphism least Let G marriage theorem matching maximal Menger's theorem minimal minimum degree multigraph neighbours normal spanning tree number of edges pair path in G planar plane graph proof of Theorem Proposition prove random graph rays regularity lemma satisfies separator sequence set of vertices spanning tree subgraph of G subset topological minor tree-decomposition tree-width Tutte's vertex vertex set well-quasi-ordered