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Diestel R. — Graph theory
Diestel R. — Graph theory

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Название: Graph theory

Автор: Diestel R.

Аннотация:

Graph Theory can be used at various levels. It contains all the standard basic material to be taught in a first graduate or undergraduate course. For an advanced graduate course, it includes proofs of several fundamental, deeper results, most of which thus appear in a book for the first time. To the professional mathematician, the book offers an overview of graph theory as it stands today: with its typical questions and methods, its classic results, and some of those developments that have made this subject such an exciting area in recent years.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: third edition

Год издания: 2005

Количество страниц: 410

Добавлена в каталог: 25.10.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Delta$-system      271
$\epsilon$-regular pair      176 191
$\epsilon$-regular partition      176
'Wagner's Conjecture'      see graph minor theorem
,-chromatic      111 134
3-colour theorem      see three colour theorem
4-colour theorem      see four colour theorem
5-colour theorem      see five colour theorem
Above      15
Abstract dual      105—106 108
Abstract graph      3 83 86 92 302
Acyclic      13—14 48 134
Adhesion      340 341
Adjacency matrix      28 32
Adjacent      3
Aharoni, R.      217 223 225 226 245 247 248
Ahuja, R.K.      161
Algebraic colouring theory      137
Algebraic flow theory      144—159 161
Algebraic graph theory      23—28 32
Algebraic planarity criteria      101—102
Algorithmic graph theory      161 349 355—356
Almost      302 312—313
Alon, N.      10 32 122 137—138 314
Alternating path      34 224
Alternating walk      64
Andreae, Th.      207 245 246
Antichain      51 53 241 316 388 389
Antihole      138
Apex vertices      340 353
Appel, K.      137
Arboricity      46—49 115 190 235 250
ARC      84 229 243 247 248 361 385
Arc-component      229 243
Arc-connected      229 243 248
Archdeacon, D.      355
Arnborg, S.      355
Articulation point      see cutvertex
AT      2
Augmenting path for matching      34 51 224 241 371
Augmenting path for network flow      143 160
Automorphism      3 31 215 239 374
Average degree      5
Average degree and choice number      122
Average degree and chromatic number      117 122 169 172 190
Average degree and connectivity      12
Average degree and girth      8 9—10 301
Average degree and list colouring      122
Average degree and minimum degree      5—6
Average degree and number of edges      5
Average degree and Ramsey numbers      273
Average degree and regularity lemma      176 191
Average degree of bipartite planar graph      376
Average degree, bounded      273
Average degree, forcing minors      163 170—171 191 192—194
Average degree, forcing topological minors      70 169—
Back-and-forth technique      213—214 383
Bad sequence      316 354
Balanced      308
Bauer      291
Behzad, M.      138
Bellenbaum, P.      355
Below      15
Berge, C.      128
Berger, E.      217 247
BETWEEN      6 84
Biggs, N.L.      32
Binary tree      203 238
Bipartite graphs      17—18 31 107 111 127
Bipartite graphs in Ramsey theory      263—264 272
Bipartite graphs, edge colouring of      119 135 136
Bipartite graphs, flow number of cubic      150
Bipartite graphs, forced as subgraph      169 183
Bipartite graphs, list-chromatic index of      125—126 138
Bipartite graphs, matching in      34—39 222—224
Birkhoff, G.D.      137
Block      55 108 372
Block graph      56 78 372
Boehme, T.      81 193
Bollobas, B.      54 80 192 193 245 272 291 304 305 313 314 356
BOND      25 31 56 104—106 110 238
Bond space      see cut space
Bond-cycle duality      104—106 152—154
Bondy, J.A.      291
Boundary of a face      89—90 107 363
Boundary of a wave      218
Boundary, circle      361
Bounded graph conjecture      238 239 244—245
Bounded subset of $\mathbb{R}^2$      86 361
Bramble      322—324 351 353 355
Bramble number      324
Bramble, order of      322
Branch in tree-decomposition      325
Branch set      19
Branch vertex      20
Brandt, S.      192
Bridge      11 41 141 151 156—157
Bridge to bridge      281
Broersma      291
Brooks theorem      115 137
Brooks theorem, list colouring version      137
Brooks, R.L.      115 134
Bruhn, H.      110 247 248 278 291
Burr, S.A.      272
Cameron, P.J.      246
Capacity      142
capacity function      141
Cardinality      357
Catlin, P.A.      193
Cayley, A.      137 313
Central face in grid      342
Central vertex      9 342 369
Centre      17
Certificate      126 341 356 390
Chain      15 51 53 241 358 360
Chebyshev inequality      308 388
Cherlin, G.      246
Choice number      121
Choice number and average degree      122
Choice number of bipartite planar graphs      135
Choice number of planar graphs      122
Chord      8
Chordal      127—128 136 326 352 391
Chordal, supergraph      391
Chromatic index      112 119
Chromatic index and maximum degree      119—121
Chromatic index of bipartite graphs      119
Chromatic index vs. list-chromatic index      121 124
Chromatic number      111 134 155 201 244 353
Chromatic number and $K^r$-subgraphs      116—117 126 226
Chromatic number and average degree      117 122 169 172 190
Chromatic number and colouring number      115
Chromatic number and connectivity      116—117
Chromatic number and flow number      155
Chromatic number and girth      117 137 175 301
Chromatic number and maximum degree      115
Chromatic number and minimum degree      115 116
Chromatic number and number of edges      114
Chromatic number as a global phenomenon      117 126
Chromatic number in extremal graph theory      168
Chromatic number of almost all graphs      304
Chromatic number vs. choice number      121
Chromatic number, constructions      117—118 134 137
Chromatic number, forcing a triangle      135 271
Chromatic number, forcing minors      172—175 190 191 193—194
Chromatic number, forcing short cycles      117 301
Chromatic number, forcing subgraphs      116—117 238 271
Chromatic polynomial      134 162
Chudnovsky, M.      128 138
Chvatal, V.      256 278 279 291
Circle in graph with ends      106 230 231 361
Circle in surface      348 361 362 365
Circle, boundary circle      361
Circle, one/two-sided      362
Circle, unit circle $S^1$      361
Circuit      23 231 242
Circulation      140—141 153 162
Circumference      8 351
Circumference and connectivity      79 276
Circumference and minimum degree      8
Class 1 vs. class 2      121
Classification of surfaces      361— 362
Clique number      126—133 263 326
Clique number of a random graph      296
Clique number, threshold function      312
Closed under addition      144 232
Closed under infinite sums      235
Closed under isomorphism      3 302 327
Closed up or down, in tree-order      15
Closed walk      10 22
Closed wrt. minors      135 160 245 327 341 342 349 352
Closed wrt. subgraphs      126 135
Closed wrt. supergraphs      126 305
Closure (of a set)      227
Cocycle      see cut
Colour class      111
Colour-critical      see critically k-chromatic
Colouring      111—138 173 201
Colouring algorithms      114 133
Colouring and flows      152—155
Colouring in Ramsey theory      253
Colouring number      114 134 135 245
Colouring plane graphs      112—113 152—155
Colouring, total      135 138
Comb      196 242
Comb, modified      240
Comb, star-comb lemma      204
Combinatorial isomorphism      93 94 107 108
Combinatorial set theory      250 272
Comfort, W.W.      250
Compactness      201 227 229 242
Compactness, proof technique      200 235—237 238 245
Comparability graph      127 136
Compatible separations      351
Complement and perfection      129 376
Complement of a bipartite graph      127 135
Complement of a graph      4
Complement of a property      327 341
Complete bipartite graph      17
Complete graph      3 150
Complete infinite graph      197 341
Complete matching      see 1-factor
Complete minor      97 101 169—175 190 191 193—194 340—341 347—348
Complete multipartite graph      17 167
Complete part of path-decomposition      352
Complete part of tree-decomposition      326
Complete r-partite graph      17
Complete separator      325 352
Complete subgraph      117 126—127 163—167 296 312 321
Complete topological minor      67—70 81 97 101 109 169—170 172 175 190 194
Complexity theory      127 341 356
Component      11 229 361
Connected      10
Connected and vertex enumeration      10 14
Connected, 2-connected graphs      55—57 78 89 94 270 281
Connected, 3-connected graphs      57—62 78 89 96 97 102 269 270
Connected, 4-connected graphs      108 270 278
Connected, arc-connected      229 243 248
Connected, infinitely connected      197 237 244
Connected, k-connected      11 12 67 79
Connected, k-connected, externally      329 352
Connected, minimally connected      14
Connected, minimally k-connected      80
Connected, semiconnected      535—236
Connected, topologically      229
Connectedness      10 14
Connectivity      11 10—13 55—81
Connectivity and average degree      12
Connectivity and chromatic number      116—117
Connectivity and circumference      79
Connectivity and edge-connectivity      12
Connectivity and girth      237 301
Connectivity and Hamilton cycles      277—278
Connectivity and linkability      70—71 80 81
Connectivity and minimum degree      12 249
Connectivity and plane duality      108
Connectivity and plane representation      96
Connectivity and Ramsey properties      268—270
Connectivity in infinite graphs      216—226
Connectivity in infinite graphs, forcing minors      354
Connectivity of a random graph      303
Connectivity via spanning trees      46 54
Connectivity, external      325 329 352 353 390
CONTAINS      3
Continuum many      357
Contraction      18—21
Contraction and 3-connectedness      58—59
Contraction and minors      18—21
Contraction and tree-width      320 321
Contraction in multigraphs      28—30 160
Convex drawing      99 107 109 386
Convex polygon      271
Core      376
Corneil, D.G.      355
Cornuejols, G.      138
Countable graph      2
Countable set      357
Countably infinite      357
Cover by antichains      53
Cover by chains      51
Cover by edges      136
Cover by paths      49—51 223
Cover by trees      49 106 250
Cover by vertices      33 34—35 44—46 322 338
Cover of a bramble      322
Critical      134
Critically k-chromatic      134 375 380
Cross-edges      24 46 235
Crosscap      362 364
Crosses in grid      322
Crown      269—270
Cube of a graph, $G^3$      290
Cube, d-dimensional      30 313
Cubic graph      5
Cubic graph, 1-factor in      41 52
Cubic graph, connectivity of      79
Cubic graph, flow number of      150 151 157 161 162
Cubic graph, multigraph      44 52 157 282
Cuff      339
Curran, S.      54
Cut      24
Cut in network      142
Cut, capacity of      142 143
Cut, even/odd      233 243 244 249
Cut, flow across      141
Cut, fundamental      26 32 231 243
Cut, minimal      25 31 56 104
Cut, space      25—28 31 32 101 105 249
Cut-cycle duality      104—106 152—154
Cut-edge      see bridge
Cutvertex      11 55—56
CYCLE      7—8
Cycle in multigraphs      29
Cycle space      23—28 31 32 59—62 101—102 105 107 109 232—235 243 244 248 249 374
Cycle space, topological      232—235 248 249
Cycle threshold function      311 313
Cycle with orientation      152—154
Cycle, directed      134 135
Cycle, disjoint cycles      44—45
Cycle, double cover conjecture      157 160
1 2 3 4 5
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