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Diestel R. — Graph Decompositions
Diestel R. — Graph Decompositions

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Название: Graph Decompositions

Автор: Diestel R.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 239

Добавлена в каталог: 18.11.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$a$-closure      158-160
$H_{0}$      56-57
$H_{0}’$      58-59
$H_{0}’’$      62-63
$H_{1}$      101-102 112
$H_{2}$      104-105 112
$k$-colouring      41 175
$k$-sum      199
$k$-sum, simplicial      182
$k$-tree      177
$K_{5}$ minor (excluded)      1 178
$Q$      97
$T$-shield      113
$X - Y$ path      10
$\aleph_{0}$-closure      173
$\mathcal{P}$-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$\acute{a}$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 ($\dag$)      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 $K_{5}$ minor      1
Excluded $K_{a}$ minor      171
Excluded $K_{\aleph_{0}}$ minor      173-174
Excluded $TK_{a}$      159-160 170-171
Excluded $TK_{\aleph_{0}}$      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${\o}$rgensen, L. K.      187
Jakobsen, I.T.      187
Jung, H. A.      171 195
Komj$\acute{a}$th, 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, $X - Y$      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 $k$-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 $TK_{a}$      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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