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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 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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 2000

Количество страниц: 322

Добавлена в каталог: 10.02.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Delta$-system      209
$\epsilon$-regular, pair      153 166
$\epsilon$-regular, partition      153
3-colour theorem      (see Three colour thm.)
4-colour theorem      (see Four colour thm.)
5-colour theorem      (see Five colour thm.)
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— 178
Bad sequence      252 280
Balanced      243
Behzad, M.      122
Berge graph      117
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, R.L., theorem      99
Brooks, R.L., 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
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 $K^{r}$-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 S      2 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 under addition      128
Closed under isomorphism      238 263
Closed wrt. minors      119 144 263
Closed wrt. subgraphs      119
Closed wrt. supergraphs      241
Closed, walk      9 19
Cocycle space      (see Cut space)
Colour class      95
Colour-critical      (see Critically k-chromatic)
Colouring      95—122
Colouring and flows      136—139
Colouring in Ramsey theory      191
Colouring, algorithms      98 117
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
Conjecture      119 122
Connected      9 2
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 external      264 280
Connectivity of a random graph      239
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 d-dimensional      26 248
Cube of a graph, $G^{3}$      227
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, capacity of      126
Cut, flow across      125
Cut, minimal      22 88
Cut, space      22—24 28 85 89
Cut-cycle duality      136—138
Cut-edge      (see Bridge)
Cutvertex      10 43—44
CYCLE      7—9
Cycle in multigraphs      25
Cycle with      136—137
Cycle with orientation      136—138
Cycle, directed      119
Cycle, double cover conjecture      141 144
Cycle, expected number      234
Cycle, Hamilton      144 213—228
Cycle, induced      7—8 21 47 86 111 117 290
Cycle, length      7
Cycle, long      8 26 64 118
Cycle, non-separating      47 86
Cycle, odd      15 99 117 290
Cycle, short      101 179—180 235 237
Cycle, space      21 23—24 27—28 47—49 85— 86 89 92—93
Cycle, threshold function      247
Cycle-cut duality      136—138
Cyclomatic number      21
Degeneracy      (see Colouring number)
Degree      5
Degree, sequence      216
Deletion      4
Dense graphs      148 150
Density of pair of vertex sets      153
Density, edge density      148
Density, upper density      166
Depth-first search tree      13 27
Deuber, W.      197
Diameter      5 9 248
Diameter and girth      8
Diameter and radius      9
Diestel, R.      186 281
Difference of graphs      4
Digon      (see Double edge)
Digraph      (see Directed graph)
Dilworth, R.P.      40 285 294
Dirac, G.A.      111 186 187 214 226
Directed, cycle      119
Directed, edge      25
Directed, graph      25 108 119
Directed, path      39
Direction      124
Disjoint graphs      3
Distance      8
Double, counting      75 92 114—115 234 244
Double, edge      25
Double, wheel      208
Drawing      67 76—80
Drawing, convex      92
Drawing, straight-line      90
Dual and connectivity      91
Dual, abstract      55—89 91
Dual, plane      87 91
Duality of plane multigraphs      87—89
Duality, cycles and cuts      23—24 88—89 136
Duality, flows and colourings      136—139 291
EDGE      2
Edge colouring      96 103—105 191
Edge colouring and flow number      135
Edge colouring and matchings      119
Edge contraction      16
Edge contraction and 3—connectedness      45
Edge contraction in multigraph      25
Edge contraction vs. minors      17
Edge cover      119
Edge density      5 148
Edge density and average degree      5
Edge density and regularity lemma      154 166
Edge density, forcing minors/topological minors      169—180
Edge density, forcing subgraphs      147—167
Edge of a multigraph      25
Edge space      20 85
Edge, crossing a partition      21
Edge, directed      25
Edge, double      25
Edge, plane      70
Edge, X — Y edge      2
1 2 3 4
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