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Diestel R. — Graph Theory

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Название: Graph Theory

Автор: Diestel R.

Аннотация:

This book is a concise, yet carefully written, introduction to modern graph theory, covering all its 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. This second edition extends the first in two ways. It offers a thoroughly revised and updated chapter on graph minors, which now includes full new proofs of two of the central Robertson-Seymor theorems (as well as a detailed sketch of the entire proof of their celebrated Graph Minor Theorem). Second, there is now a section of hints for all the exercises, to enhance their value for bith individual study and classroom use.

Язык:

Рубрика: Математика/Алгебра/Комбинаторика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second edition

Год издания: 2000

Количество страниц: 312

Добавлена в каталог: 07.12.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

, ...      232
$(S,\bar{S})$ , ...      126
      7
      108
$Forb_{\preccurlyeq}(\chi)$       257
$f^\ast(v)$       88
      196
, , ...      216
$G^\ast$ , $F^\ast$ , $\vec{e}^\ast$ , ...      88 136 140
      3
      14
$K_{n_1,...,n_r}$       14
      108
      6
      118
      191
      161
      69
$T^{r-1}(n)$       149
$t_{r-1}(n)$       149
$v^\ast(f)$       88
, $v_{xy}$ ,       15 16
$[\quad]$       4 72
$[\quad]^k$ , $[\quad]^{<\omega}$       1 250
$\alpha(G)$       110
$\ast$       4
$\bar{0}$ , $\bar{1}$ , $\bar{2}$ , ...      1
$\bar{G}$ , $\bar{X}$ , $\bar{\mathcal{G}}$ , ...      4 124 258
$\bar{i}$       1
$\cap$       3
$\chi''(G)$       119
$\chi'(G)$       96
$\chi(G)$       95
$\cup$       3
$\delta(G)$       5
$\dot{P}$ , $\dot{x}Q$ , ...      7 68
$\emptyset$       2
$\epsilon$ -regular pair      153 166
$\epsilon$ -regular partition      153
$\in$       2
$\kappa(G)$       10
$\kappa_G(H)$       56
$\lambda(G)$       11
$\lambda_G(H)$       56
$\langle\, ,\, \rangle$       19
$\large{\nu}(G)$       19
$\lceil\, \rceil$       1
$\leq$       251
$\lfloor\, \rfloor$       1
$\mathbb{F}_2$       19
$\mathbb{N}$       1
$\mathbb{Z}_n$       1
$\mathcal{C}(G)$       20
$\mathcal{C}^\ast(G)$       21
$\mathcal{C}^\bot$ , $\mathcal{F}^\bot$ , ...      19
$\mathcal{C}_G$       34
$\mathcal{E}(G)$       21
$\mathcal{G}(n,p)$       228
$\mathcal{P}_H$       241
$\mathcal{P}_{i,j}$       236
$\mu$       240
$\omega(G)$       110
$\overleftarrow{e}$ , $\overleftarrow{E}$ , $\overleftarrow{F}$       124
$\pi: S^2\setminus{(0,0,1)}\rightarrow\mathbb{R}^2$       69
$\preccurlyeq$       16
$\sigma^2$       240
$\sigma_k: \mathbb{Z}\rightarrow\mathbb{Z}_k$       131
$\simeq$       3
$\subseteq$       3
$\triangle$ -system      209
$\triangle(G)$       5
$\varepsilon(G)$       5
$\varphi(G)$       131
$\vec{E}$ , $\vec{F}$ , $\vec{C}$ , ...      124 136 138
$\|\quad\|$       2 153
$|\quad|$       2 126
(e,x,y), ...      124
+      4 19 128
-      4 70 128
/      15 16 24
1-edge-connected      10
3-colour theorem      see “Three colour thm.”
4-colour theorem      see “Four colour thm.”
5-colour theorem      see “Five colour thm.”
=      3
Abstract, dual      55—89
Abstract, graph      3 67 76 238
Acyclic      12 60
Adjacency matrix      24
Adjacent      3
Ahuja, R.K.      145
Algebraic colouring theory      121
Algebraic flow theory      128—143
Algebraic graph theory, ix      20—25 28
Algebraic planarity criteria      85—86
Algorithmic graph theory      145 276—277 281—282
Almost      238 247—248
Alon, N.      106 121—122 249
Alternating path      29
Alternating walk      52
Antichain      40 41 42 252
Appel, K.      121
Arboricity      61 99 118
ARC      68
Archdeacon, D.      281
Articulation point      see “Cutvertex”
AT      2
Augmenting path for matching      29 40 285
Augmenting path for network flow      127 144
Automorphism      3
Average degree      5
Average degree and chromatic number      101 106 178 185
Average degree and connectivity      11
Average degree and girth      237
Average degree and list colouring      106
Average degree and minimum degree      5—6
Average degree and number of edges      5
Average degree and Ramsey numbers      210
Average degree and regularity lemma      154 166
Average degree of bipartite planar graph      289
Average degree, bounded      210
Average degree, forcing minors      169 179 184
Average degree, forcing topological minors      61 170—
Bad sequence      252 280
Balanced      243
Behzad, M.      122
Berge graph      111
Berge, C      117
BETWEEN      6 68
Biggs, N.L.      28
Bipartite graphs      14—15 27 91 95
Bipartite graphs in Ramsey theory      202—203
Bipartite graphs, edge colouring of      103 119
Bipartite graphs, flow number of cubic      133—134
Bipartite graphs, forced as subgraph      152 160
Bipartite graphs, list-chromatic index of      109—110 122
Bipartite graphs, matching in      29—34
Birkhoff, G.D.      121
Block      43
Block, graph      44 64
Bohme, T.      66
Bollobas, B.      28 65 66 166 170 210 227 228 240 241 249 250
BOND      see “(Minimal) cut”
Bond space      see “Cut space”
Bondy, J.A.      228
Boundary of a face      72—73
Bounded subset of $\mathbb{R}^2$       70
Bramble      258—260 281
Bramble, number      260 278
Bramble, order of      258

Branch, set      16
Branch, vertex      18
Bridge      10 36 125 135 215
Bridge to bridge      218
Brooks, R.L.      99 118
Brooks, theorem      99
Brooks, theorem, list colouring version      121
Burr, S.A.      210
Capacity      126
Capacity, function      125
Catlin, P.A.      187
Cayley, A.      121 248
Central vertex      9 283
Certificate      111 274 282
ch'(G)      105
ch(G)      105
Chain      13 40 41
Chebyshev inequality      243 295
Chen, G.      210
Choice number      105
Choice number and average degree      106
Choice number of bipartite planar graphs      119
Choice number of planar graphs      106
Chord      7
Chordal      111—112 120 262 279
Chromatic index      96 103
Chromatic index and maximum degree      103—105
Chromatic index of bipartite graphs      103
Chromatic index vs. list-chromatic index      105 108
Chromatic number      95 139
Chromatic number and -subgraphs      100—101 110—111
Chromatic number and average degree      101 106 178 185
Chromatic number and connectivity      100
Chromatic number and extremal graphs      151
Chromatic number and flow number      139
Chromatic number and girth      101 237
Chromatic number and maximum degree      99
Chromatic number and minimum degree      99 100
Chromatic number and number of edges      98
Chromatic number as a global phenomenon      101 110
Chromatic number of almost all graphs      240
Chromatic number vs. choice number      105—106
Chromatic number, forcing a triangle      119 209
Chromatic number, forcing minors      181—185
Chromatic number, forcing short cycles      101 237
Chromatic number, forcing subgraphs      100—101 178 209
Chromatic polynomial      118 146
Chvatal, V.      194 215 216 228
Circle on       70
Circuit      see “Cycle”
Circulation      124 137 146
Circumference      7
Circumference and connectivity      64 214
Circumference and minimum degree      8
Class 1 vs. class 2      105
Clique number      110—117 202 262
Clique number of random graph      232
Clique number, threshold function      247
Closed walk      9 19
Closed, under addition      128
Closed, under isomorphism      238 263
Closed, wrt. minors      119 144 263
Closed, wrt. subgraphs      119
Closed, wrt. supergraphs      241
Cocycle space      see “Cut space”
col(G)      99
Colour class      95
Colour-critical      see “Critically k-chromatic”
Colouring      95—122
Colouring algorithms      98 117
Colouring and flows      136—139
Colouring in Ramsey theory      191
Colouring number      99 118 119
Colouring plane graphs      96—97 136—139
Colouring total      119
Combinatorial isomorphism      77 78
Combinatorial set theory      210
Compactness argument      191 210
Comparability graph      111 119
Complement and perfection      112 290
Complement of a bipartite graph      111 119
Complement of a graph      4
Complement of a property      263
complete      3
Complete, bipartite      14
Complete, matching      see “1-factor”
Complete, minor      179—184 275
Complete, multipartite      14 151
Complete, part of path-decomposition      279
Complete, part of tree-decomposition      262
Complete, r-partite      14
Complete, separator      261 279
Complete, subgraph      101 110—111 147—151 232 247 257
Complete, topological minor      61—62 170—178 184 186
Complexity theory      111 274 282
Component      10
Connected      9
Connected and vertex enumeration      9 13
Connected, 2-connected graphs      43—45
Connected, 3-connected graphs      45—49 79—80
Connected, k-connected      10 64
Connected, k-connected, externally      264 280
Connected, minimally connected      12
Connected, minimally k-connected      65
Connectedness      9 12 297
Connectivity      10—11 43—66
Connectivity and average degree      11
Connectivity and circumference      64
Connectivity and edge-connectivity      11
Connectivity and girth      237
Connectivity and Hamilton cycles      215
Connectivity and linkability      62 65
Connectivity and minimum degree      11
Connectivity and plane duality      91
Connectivity and plane representation      79—80
Connectivity of a random graph      239
Connectivity, external      264 280
Connectivity, Ramsey properties      207—208
CONTAINS      3
Contraction      16—18
Contraction and 3-connectedness      45—46
Contraction and minors      16—18
Contraction and tree-width      256
Contraction in multigraphs      25—26
Convex, drawing      82 90 92
Convex, polygon      209
Core      289
Cover by antichains      41
Cover by chains      40 42
Cover by edges      119
Cover by paths      39—40
Cover by trees      60—61 89
Cover by vertices      30 258
Cover of a bramble      258
Critical      118
Critically k-chromatic      118 293
Cross-edges      21 58
Crosses in grid      258
Crown      208
Cube of a graph,       227
Cube, d-dimensional      26 248
Cubic graph      5
Cubic graph, 1-factor in      36 41
Cubic graph, connectivity of      64
Cubic graph, flow number of      133—134 135
Cut      21
Cut in network      126
Cut space      22—24 28 85 89
Cut, capacity of      126
Cut, flow across      125

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