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| Diestel R. — Graph Theory |
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| Предметный указатель |
 -system 209
 -regular, pair 153 166
-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  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  -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,  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
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