Random GraphsThis is a new edition of the now classic text. The already extensive treatment given in the first edition has been heavily revised by the author. The addition of two new sections, numerous new results and 150 references means that this represents an up-to-date and comprehensive account of random graph theory. The theory estimates the number of graphs of a given degree that exhibit certain properties. It not only has numerous combinatorial applications, but also serves as a model for the probabilistic treatment of more complicated random structures. This book, written by an acknowledged expert in the field, can be used by mathematicians, computer scientists and electrical engineers, as well as people working in biomathematics. It is self contained, and with numerous exercises in each chapter, is ideal for advanced courses or self study. |
Contents
IV | 1 |
V | 5 |
VI | 9 |
VII | 15 |
VIII | 25 |
IX | 34 |
XI | 43 |
XII | 46 |
L | 243 |
LI | 245 |
LII | 248 |
LIII | 251 |
LVI | 254 |
LVII | 264 |
LVIII | 267 |
LIX | 271 |
XIII | 50 |
XIV | 60 |
XV | 65 |
XVI | 69 |
XVII | 72 |
XVIII | 74 |
XIX | 78 |
XX | 79 |
XXI | 85 |
XXII | 91 |
XXIII | 96 |
XXV | 102 |
XXVI | 110 |
XXVII | 117 |
XXVIII | 130 |
XXIX | 138 |
XXX | 143 |
XXXI | 148 |
XXXII | 153 |
XXXIII | 160 |
XXXIV | 161 |
XXXV | 166 |
XXXVI | 171 |
XXXVII | 178 |
XXXVIII | 189 |
XXXIX | 195 |
XL | 201 |
XLII | 202 |
XLIII | 206 |
XLIV | 212 |
XLV | 219 |
XLVI | 221 |
XLVII | 224 |
XLVIII | 229 |
XLIX | 241 |
LX | 276 |
LXI | 282 |
LXII | 290 |
LXIII | 294 |
LXIV | 298 |
LXV | 303 |
LXVI | 319 |
LXVIII | 320 |
LXIX | 324 |
LXX | 332 |
LXXI | 339 |
LXXII | 341 |
LXXIII | 348 |
LXXVI | 357 |
LXXVII | 365 |
LXXVIII | 373 |
LXXIX | 376 |
LXXX | 383 |
LXXXI | 384 |
LXXXII | 394 |
LXXXIII | 399 |
LXXXIV | 408 |
LXXXV | 412 |
LXXXVI | 425 |
LXXXVIII | 426 |
LXXXIX | 431 |
XC | 435 |
XCI | 442 |
XCII | 447 |
XCIII | 448 |
XCIV | 451 |
XCV | 455 |
| 457 | |
| 496 | |
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Common terms and phrases
1-factors a.e. Gp A₁ asymptotic bipartite graph Bollobás c₁ Chapter Chebyshev's inequality chromatic number clique number colour component of order conference graphs constant Corollary cubic graphs d₁ define Denote diameter disjoint distribution elements Erdős and Rényi expected number fixed Frieze Furthermore G₁ Gc/n giant component Gk-out Gn,p Gr-reg graph G graph of order greedy algorithm H₁ Hamilton cycles Hamiltonian Hence implies induced subgraph inequality integer isomorphic k-core k₁ labelled graphs Lemma log log log2 logn lower bound M₁ maximal minimum degree n₁ natural number number of vertices Paley graph Poisson Poisson distribution probability space proof of Theorem proved r-regular graph r.vs random graphs result satisfies subgraph sufficiently large Suppose T₁ Theorem threshold function tree components trees of order triangle-free graph upper bound V₁ vertex set vertices of degree X₁