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Bollobas B. — Modern Graph Theory
Bollobas B. — Modern Graph Theory



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Название: Modern Graph Theory

Автор: Bollobas B.

Аннотация:

This book is an in-depth account of graph theory; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory - An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 394

Добавлена в каталог: 12.03.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Graph, k-edge-connected      73
Graph, Kneser      170 285
Graph, minor      24
Graph, Moore      106
Graph, order of      3
Graph, oriented      8
Graph, outerplanar      36
Graph, perfect      146 165
Graph, permutation      175
Graph, Petersen      106 170 272
Graph, planar      20 21
Graph, plane      20
Graph, r-partite      6
Graph, radius of      10
Graph, randomly Eulerian      19 32
Graph, realization      21
Graph, regular      4
Graph, simple      7
Graph, simplicial      175
Graph, size of      3
Graph, strongly regular      274
Graph, Thomsen      23
Graph, topological      21
Graph, triangulated      175
Graph, trivial      3 183
Graph, vertex-transitive      291
Graphic sequence      96
Greedy algorithm      147
Grfitzsch graph      285
Griinwald, T.      20 36
Grimmett, G.      377
Grotschel, M.      144 179 213
Group, finitely presented      255
Group, free      255
Group, McLaughlin      276
Group, sporadic simple      276
Group, Suzuki      276
Guthrie, R      159
Gyarfas, A.      143
Hadwiger, H.      159
Hajnal, A.      214
Hajos sum      173
Hajos, G.      178
Haken, W.      154 159 160 178
Hales — Jewett theorem      200
Hales, A.      382 199 214
Hall, P.      67 77 101
Hall’s marriage theorem      67 77
Halmos, P.R.      77
Hamilton, cycle      14
Hamilton, path      14
Hamilton, Sir William Rowan      14
Hamiltonian      343
Handshaking lemma      4
Harary, F      213 293
Harmonic function      301
Harrington, L.      189 213
Heawood bound      156
Heawood, P.J.      156 159
Heesch, H.      159 178
HeiIbronn, H.A      253
Higman, G      292
Hilbert.D.      197 198
Hindman, N.      182 207 214
Hindman’s theorem      207
Hitting time      235 305 312
Hoffman — Singlecon theorem      275
Hoffman, A, J.      275 292
Hopf link      369
Hypergraph      7
Incidence matrix      54
incident      2
Independence number      147
Independent      4
INDEX      260
Integrality theorem      71
Internal activity      350
Ising model      544
Isomorphic      3
Isomorphism problem      256
Isotopy, regular      360
Isthmus      370
Janson, S.      242 246 252 377
Jensen, T.R.      179
Jerrum, M.R.      334
Jewett, R.I.      182 199 214
Join      1
Jones polynomial      366
Jones, V.R R.      359 378
k-book      35
k-closure      116
k-cup      185
k-regular      4
k-stable      116
Kahn, J.      165 178
Kainen, P.C      159 178
Kakutani, S.      333
Kaliningrad      16
Kannan, R.      334
Kant, E.      16
Karass, A      291
Karp, R.M.      242 333
Kasteieyn, P.W.      344 377
Katona, G.      64 178
Kauffman, angle bracket      364
Kauffman, bracket      364
Kauffman, L.H.      378
Kauffman, polynomial      366
Kauffman, square bracket      363
Kazarinoff, N.D.      66
Kempe chain      159
Kempe, A B.      159
Kim, J.H.      221
Kirchhoff’s, current law      40 296
Kirchhoff’s, potential law      40 296
Kirchhoff’s, theorem      44 296
Kirchhoff’s, voltage law      40
Kirkman, T.      101
Kirkman, T.P.      37 358 377
Klein, bottle      155
Klein, four-group      172
Knot      258 359
Knot, amphicheiral      367
Knot, chiral      367
Knot, knotted      361
Knuth, D.E.      102 242 246 252
Koch, J.      178
Komlos, J.      135 144 221 239 251 252
Konig, D.      36 67 77 165
Konigsberg      16 40
Korshunov, A.D.      239 252
Ktrchhoff, G.      40 55 66
Kuratowski, K,      24 37
l-cap      185
l-cube      198
l-cycle      5
L-edge-colouring      163
l-factor      68
Lagrangian      265
Laplacian, analytic      288
Laplacian, combinatorial      268
Latin, rectangle      94
Latin, square      95
Lazy random walk      321
Leech, J.      292
Lemma of Burnside      278 292
Lemma of Cauchy and Frobenius      278 292
Lemma of Posa      118
Lemma of Szemeredi      104 122 129
Length      4 5
Levitzki, J.      25 37
Li, Y.      193 214
Line graph      93 165
Link      359
Link, ambient isotopic      359
Link, diagram      359
Link, equivalence      359
Link, linked      361 374
Link, oriented      359
Link, split      374
Lipton, R.J.      333
List-chromatic, index      163
List-chromatic, number      161
List-edge-chromatic number      163
Listing, J.B.      11 377
Little, C.N.      358 359 377
Livingston, C.      378
Lollipop graph      330
Loop      7
Lovasz, L.      144 166 169 178 179 213 333 334
Luczak, T.      241 242 246 252
Mader, W.      101
Magnus, W.      291
Mantel, W.      6
Mantel’s theorem      6
MAP      22 159
Markov chain      302
Markov chain, ergodic      328
Markov chain, reversible      329
Markov’s inequality      228
Marriage theorem      78
Matching      67
Matching, complete      77
Mate, A.      214
Matrix, adjacency      54 262
Matrix, adjacency, collapsed      272
Matrix, conductance      57
Matrix, hermitian      262
Matrix, incidence      54
Matrix, Kirchhoff      54 57
Matrix, Laplacian      54 268 288
Matrix, transition probability      303
Matrix-tree theorem      57
Matroid      335
Max-flow min-cut theorem      67 70 91
Maximal matching      85
Maximum Modulus Principle      328
McKay, B.D.      185 213
Mean, commute time      314
Mean, cover time      331
Mean, hitting time      311
Mean, return time      312
Medial graph      368
Menger, K.      67 77 101
Menger’s theorem      67 75
Mihail, M.      334
Miklos, D.      144
Milman, V.      292
Milman, V.D.      334
Minor      24
Minor, forbidden      24
Monochromatic set      186
Monotone      115
Monotoniaty principle      297 301
Moore graph      106
Moron, Z.      47
Motzkin, T, S.      267 292
Multigraph      7
Multigraph, directed      8
Murasugi, K.      371 378
Nash-Williams, C.St.J.A.      333
Near-triangulation      162
Neighbouring      2
Nesetril, J.      196 213
Neumann, P.      292
Novikov, P.S.      292
Nugatory crossing      370
Nullity      53 337
Numerical range      263
Odd component      82
Ohm, G.S.      39
Ohm’s Law      39 296
Orbit      278
Orientation      54
Orientation, totally cyclic      372
Oxiey, J.G.      377 378
Pach, J.      133 144
Palmer, E.M.      293
Paris, J.      189 213
Partial order      80
Partially ordered set      80
Partition calculus      208
Partition function      343
Path      4
Path, Hamilton      14
Path, independent      4
Path, internally disjoint      4
Path, of length l      5
Pattern      279
Pattern, sum      281
Pentagon      5
Perfect graph, conjecture      169
Perfect graph, theorem      166 167
Perfect squared square      46
Perko, K.A.      358
Petersen, J.      95 159
Petersen’s theorem      95
Phase transition      240 241
Pintz, J.      251 252
Pittel, B.      242 246 252
Place      279
Plane, map      22
Pollak, H.O.      266
Polya’s enumeration theorem      278 281 308
Polynomial chromatic      151
Posa, L.      106 143 236 239 252
Potential law      296
Potential, difference      39
Potential, law      40
Potential, vector      55
Potts ferromagnetic model      342
Potts measure      343
Potts model      343
Pregel      16 19
Presentation      255
Prikry, K.      182 205 214
Principle, Dirichlet      299
Principle, double counting      45
Principle, maximum modulus      328
Principle, monotonicity      297 301
Principle, of conservation of energy      300
Principle, Rayleigh      300
Principle, stability      116
Principle, superposition      41 328
Principle, Thomson      299
Problem of Zarankiewiez      112 221
Projective plane      114 155
Proper colouring      145
Property of graphs      115
Property, monotone decreasing      232
Property, monotone increasing      232
Prtifer code      277
Prufer, E      277
Quadrilateral      5
R-factor      82
Rackoff, C      334
Rado, R.      78 182 189 213 214
Rado’s Theorem      204
Radziszowski, S.P.      185 213 214
Raghaven, P.      334
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