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| Diestel R. — Graph Decompositions |
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| Предметный указатель |
 -closure 158-160
 56-57
 58-59
 62-63
 101-102 112
 104-105 112
 -colouring 41 175
-sum 199
-sum, simplicial 182
-tree 177
 minor (excluded) 1 178
 97
 -shield 113
 path 10
 -closure 173
 -sum 199
(S1) 6
(S2) 6 175
(S3) 6 40 93 164
(S4) 6 26 160 175
(S5) 161 175
Accessible side 55
Aharoni, R. 197
Almost all 37
Arnborg, S. 178
Attached 9 16
Attached, and maximally prime 41 52
Attached, simplex 22-23
Attached, weakly 129
Attachment graph 28
Beeri, C. 202
Birth of a vertex 8
Birth of components (order of) 21 35
Boland 191
Bollob s 6 187
Bound (in a partial ordering) 206
Branch set 12
Branch vertex 12
Buneman, P. 192
Cardinal 207
Cardinal, regular 208
Cardinal, successor 208
Chain 203
Chain, of order a 167-171
Chordal 96 97 188-193
Chordal closure 122
CLIQUE 96 188
Clique number 96
Close (simplicially) 12 16 103 122
Coherent decomposition 10 16 32 42
Compactness 97
COMPLEX 95
Comprehensive family 138-142
Concatenation (of well-ordered families) 12
Condition ( ) 60
Convex and unattached extension 154
Convex hull 11 16
Convex subgraph 11 13 16-17 22-23 52 163
Corneil, D. G. 178
Crossing chords 189
cube 182
Dahlhaus, E. 202
De Bruijn, N. G. 195
Decomposition tree 26 162 172
Decomposition tree, generalized 161 162 172
Defusable 74
Defuse (a side) 63
Defused at 64
Diestel, R. 34 41 60 112 146 179 184 190 193 194
Dirac, G. A. 90 197 187 188
Dirac’s theorem 90-91
Dispensable factor 127-128 130 137-139 142 147-149
Duchet, P. 200
Edge-maximal 2 172 179
Eligible 74
Empty graph 6
END 196
End, of a tree 192
Erdos, P. 187 195 197
Evolution of a graph 4 8
Evolution of a separating simplex 18-21
Excluded minor 1
Excluded  minor 171
Excluded  minor 173-174
Excluded  159-160 170-171
Excluded  173-174
Excluded minor theorems 1 178- 185
Extension into a component 10 51
Extension of a well-ordered family 13
Extremal graphs 186
Factor 9
Factor, in a simplicial decomposition 13 24
Factor, prime 9
Finite factor 4 96 126
Finite prime decomposition 47
Finite prime subgraph 41 52
Finite simplex (extension of a) 52
Finite simplex of attachment 34 41
Finite simplicial decomposition 1-2 23 26
Fulkerson, D.R. 191
Gallai, T. 189
Gavril, F. 192
Generalized decomposition tree 161
Generalized tree-decomposition 161-171
Gilmore, P. C. 191
Gross, O.A. 191
Hadwiger’s Conjecture 178
Hadwiger’s Conjecture, infinite analogue to 195
Halin, R. v viii 13 56 92 153 155 159 172 180-181 191 192 194-197
Halin’s theorem 53
Helly property 191 192
Hoffman, A. J. 191
Homomorphism 12
Homomorphism base 179
Homomorphism base, simple 183
Homomorphism, contractive 12 106
Homomorphism, simplicial 103 107-110 122
Inaccessible side 55-60 99-100 150
Incomparable factors 42
Independent paths 11
Indispensable, see dispensable induction (transfinite) 205
Initial ordinal 207
Initial part (in a decomposition) 8 13
Initial segment (of a well-ordering) 204
INTERFACE 129-130 142 150
Intersection graph 191
Interval graphs 190-191
Irreducible 2
J rgensen, L. K. 187
Jakobsen, I.T. 187
Jung, H. A. 171 195
Komjth, P. 194
Kuratowski’s Theorem 1 177
Las Vergnas, M. 200
Lauritzen, S.L. 202
Laver, R. 189
Leimer, H. - G. 201
Lekkerkerker, C. 191
Limit (in a well-ordering) 204
Maximal in a partial ordering 203
Maximal simplex 35
Maximal with respect to extension 13 55
Maximally prime 9 15-16 22-24
| Menger number 11 153-159 172 173
Menger’s theorem 158 197
Meyniel, H. 200
Minimal in a partial ordering 203
Minimal relative separator 10 25 41
Minimal side 55
Minimally convex 11 21-24 40
Minor 12 102
Minor relation 102-104 122
Minor, simplicial 104 109-110 112 122
Monotone limit 13 53 93 127- 129 137-138
Neighbourhood (simplicial) 12 17 41
Null-homotopic 200-201
octahedron 182
Odd cycles 189
One-defusable 75
Order in a rooted tree 27
Order of factors, in a prime decomposition 125
Order of factors, in a simplicial decomposition 4
Order of factors, in a simplicial tree-decomposition 27-29
Order type 204
Order-theoretical forest 161 172
Order-theoretical subtree 168 173
Order-theoretical tree 43 161 172
Ordinal 204
Pach, J. 194
Partial ordering 203
Perfect graphs 189
Planar graphs 1 184
Plane triangulations 2 180-181 190
Predecessor 203
Prime decomposition 9 16 19-21
Prime decomposition, existence of a 53 60 90-91 112
Prime decomposition, reduced 127 146-149
Prime decomposition, uniqueness of a 125-129 142-147
Prime extension 50-52
Prime factor 9
Prime factor, in a simplicial decomposition 24
Prime graph 9 15
Prime subgraph 16 22-23
prism 182
Problems (open) 3-4 90 123 149 172 173-174 183-185
Proskurowski, A. 178
Rado, R. 193
Rearrangement 28-29 42
Recursive definition 206
Reduced prime decomposition 127 148-149
Regular cardinal 208
Robertson, N. 2-3 42 177 185
Rooted-tree order 27
Semitopological graphs 186
Separating simplex 15
Separating simplex, and prime decomposition 56-60
Separating simplex, evolution of a 18-21
Separation properties 29-33
Separator, 10
Separator, minimal relative 10 25 41
Seymour, P. D. 2-3 42 177 185
Shadow 178 197
sides 54-55
Sides, accessible 55
Sides, inaccessible 55-60 99-100 150
Sides, minimal 55
Sides, partial order of 55
Simple homomorphism base 183
simplex 9
Simplex of attachment 9 25 41 142-144
Simplex, as a factor 24 130 139
Simplex, attached 22-23 35
Simplex, extending a finite 52
Simplex, in a prime graph 15
Simplex, maximal 35
Simplex, separating see there simplex, unattached 23 35
Simplicial -sum 182
Simplicial decomposition 6
Simplicial decomposition, consecutive 191
Simplicial decomposition, into finite factors 4 96
Simplicial decomposition, into small factors 155
Simplicial decomposition, vs. simplicial tree-decomposition 26 34
Simplicial decomposition, vs. tree-decomposition 176
Simplicial homomorphism 103 107-110 122
Simplicial minor 104 109-110 112 122
Simplicial neighbourhood 12 17 41
Simplicial tree-decomposition 6
Simplicial tree-decomposition, vs. simplicial dec 26 34
Simplicially close 12 16 103 122
Small subgraph 151
Speed, T. P. 202
Spiegelhalter, D. J. 202
Strongly unattached 129-130 142
Structural characterization 3
Structure theorem for graphs without a 170-171
Structure theorem for simplicial tree-decompositions 35
Subdividing vertex 12
Subdivision 12
Subdivision, base 183
Subtrees, family of 192
Subtrees, order-theoretical 163 173
Successor 203
Sum of cardinals 207
Sum of ordinals 205
Sum, connected 199
Sum, simplicial 199
Tarjan, R. E. 201
Thomas, R. 97
Thomassen, C. 187
Toft, B. 187
Transfinite induction 205
Tree (order-theoretical) 43 161
Tree-decomposition 6 26-33 42
Tree-decomposition, generalized 161-171
Tree-decomposition, vs. simplicial decomposition 176
Tree-decomposition, well-founded 173
Tree-representable 192-193
Tree-structure (of a graph) 2 160
Tree-width 9 96 97 178
Triangulated cycle 189
Two-defusable 75
Tychonov’s theorem 97
Unattached 9 16 24 174
Unattached, simplex 23 35
Unattached, strongly 129-130 142
Undefused 64
Universal graph 193-194
Urgent component 138 150
Vijayan, K. 202
Vogler, W. 194
Wagner graph W 178 179
Wagner, K. 1 178 180-181 187
Wagner’s conjecture 177
Wagner’s decomposition algorithm 1-2 23 45 47 95
Wagon, S. 189
Weakly attached 129
Well-connected 200
Well-founded 203
Well-founded, tree-decomposition 173
Well-ordered 203
Well-ordered, family 205
Wheel 182
Whitesides, S.H. 201
Width (of a tree-decomposition) 9
Yield (of a comprehensive family) 138-142
Zorn’s Lemma 206
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