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Bollobas B. — Modern Graph Theory

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Название: Modern Graph Theory

Автор: Bollobas B.

Аннотация:

This book is an in-depth account of graph theory; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory - An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 394

Добавлена в каталог: 12.03.2008

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Предметный указатель

$(\alpha,\omega)$ -graph      176
$\Gamma$ -orbit      278
$\varepsilon$ -uniform partition      124
$\varepsilon$ -uniforni pair      124
(k, k, g)-graph      175
Acyclic orientation      96
Adjacency matrix      54
Adjacency, matrix      262
Adjacency, matrix, collapsed      272
Adjacent      2
Ajtai, M.      221
Aldous, D.      334
Aleliunas, R.      333
Alexander, J.W.      358 359 378
Almost every      225
Alon, N.      292 293 334
Amitsur, S.A.      25 37
Anderson, I.      101
Antichain      81
Appel, K.      154 159 160 178
Attachment      59
Automorphism group      270
Babai, L.      293
Ban, R.      213
Beige, C      165
Beineke, L.W.      178
BEST theorem      19
Biggs, N.      292
Bipartite graphs      152
Bipartition      6
Birkhoff, G      159
Block      74
Boilobas — Erdos theorem      122
Bollobas, B.      102 120 135 143 179 230 234 239 241 246 251 252 292 334 377 378
Bondy, J.A.      135 116 118 143 144
Borromean rings      369
Boundary      22
Bridge      6
Brightwell.G.      334
Brinkman, J.      175
Brooks, R.L.      48 66 177
Brooks’ theorem      148
Brown, W, G.      143
Brylawski, T.H.      355 378
Bumside, W.      278 292
Burde, G.      292 378
Burr, S.A.      196 213
Cameron, P.J.      293
Capacity of a cut      69
Capacity of an edge      69
Cauchy, A.L.      278
Cayley, A.      159 276
Chain      80
Chandra, A.K.      334
Chen, G.      196
Chord      53
Chromatic index      146
Chromatic invariant      355
Chromatic number      145 156
Chromatic polynomial      151
Chromatic surplus      193
Chung, F.R.K.      197 292
Chvatal — Szemeredi theorem      122
Chvatal, V.      115 116 118 122 143 193 196 213
Circuit      5
Circulation      91
Circumference      104
CLIQUE      112 138
Clique number      112 145 230 267
Closed trail      5
Closure      116
Cocycle, fundamental      53
Cocycle, space      53
Cocycle, vector      52
Cocycle, vector, fundamental      53
College admissions problem      90
Colour class      146
Colouring      145
Colouring, irreducible      189
Colouring, S-canonical      189
Colouring, unavoidable      189
Combinatorial Laplacian      54 57
Comfort, W.W.      214
Comparability graph      166
Complement      3
Component      6
Conductance      42
Conductance, effective      300
Conductance, matrix      57
Conductance, of a graph      321
Conductance, of a network      300
Conductance, of an edge      296
Configuration      159 279
Configuration, reducible      159
Conjecture of Berge      169
Conjecture of Bollobas      135
Conjecture of Burr and Endos      196
Conjecture of Erdos and Sos      135
Conjecture of Erdos and Turan      205
Conjecture of Graham and Rothschild      207
Conjecture of Grunbaum      175
Conjecture of Hadwiger      159 171
Conjecture of Keawood      158
Conjecture of Tait      172
Conjugacy problem      256
Connection in parallel      42
Connection in series      42
Connectivity      73
Conservation of energy principle      300
contracting      336
Contraction      24 59 149 171
Conway, J.H.      376 378
Coppersmith, D.      334
Corank      54
Countries      22
Coupon collector’s problem      332
Cover      79
Cover time      331
Coxeter, H.S.M      291
Critically imperfect graphs      169
Crowell, R.H.      292
Current      40 68
Current law      296
Current, law      40
Current, total      40
Current, vector      55
Cut      52 69 72 149 350
Cut, fundamental      53
Cut, space      53
Cut, vector      52
Cut, vector, fundamental      53
Cutting      336
Cutvertex      6
CYCLE      5 350
Cycle, broken      151
Cycle, fundamental      53
Cycle, Hamilton      14
Cycle, index      280
Cycle, of length l      5
Cycle, space      52
Cycle, sum      280
Cycle, vector      52
Cycle, vector, fundamental      53
Cyclomatic number      53
de Bruijn, N.G.      19 37 50 63 64 66
De Morgan, A.      159
de Werra, D.      102
Decoration      260
Decreasing rearrangement      99
Degree      3

Degree, maximal      4
Degree, minimal      4
Degree, sequence      4
Dehn, ML      48 66 257 292 358 377
deleting      336
Deletion      149
density      123 124
Density, upper      123
Detailed balance equations      310
Diagram      359
Diagram, Cayley      254
Diagram, Schreier      254
Dichromatic polynomial      342
Dilworth, R.P.      80
Dirac, G.A.      37
Dirac’s theorem      106 107
Dirichlet’s principle      299
Distinct representatives      76
Domain      279
Domination number      136
Doubly stochastic matrix      93
Doyle, P G.      333
Duijvestijn, A.J.W.      48 61 66
Dyer, M.E.      334
EDGE      1
Edge, clique-cover number      138
Edge, externally active      350
Edge, internally active      350
Edge, multiple      7
Edge, space      51
Edge-choosability number      163
Edge-chromatic number      146
Edge-connectivity      73
Effective conductance      300
Effective resistance      300
Egervary, G.      67 77
Electrical current      39
Electrical network      39
Endblock      74
Endos — Stone theorem      120 122
Endvertex      1
Energy      298
Equitable colouring      92
Equitable partition      124
Erdos — Rado canonical theorem      190 191
Erdos, P.      20 36 98 104 110 120 135 143 178 182 185 186 189 196 204 205 209 213—216 218 221 228—230 232 234 240 246 251 252
Escape probability      304
Euler — Poincare formula      155 156
Euler, characteristic      155
Euler, circuit      16
Euler, L.      14 16 22 36
Euler, trail      16
Euler, trail, one-way infinite      32
Euler, trail, two-way infinite      20
Eulerian graph      16
Eulerian randomly      19
Euler’s formula      22
Euler’s polyhedron theorem      22
Expander      289
External activity      350
Extremal graph      103 104
Face      22
Factor      82
Fagin, R.      251
Falling factorial      220
Family, dense      206
Family, Ramsey      205
Family, thin      206
Fan      93
Fano plane      8
Feder, X      102
Fenner, T.I.      252
figure      279
Figure of eight      369
Figure, sum      280
Flow      68 347
Flow polynomial      348
Flow, nowhere-zero      347
Folkman, J.      196
Forbidden subgraph problem      103
Ford, L.R.      67 91 101
Forest      6
Fortuin, C.M.      344 377
Foster, R.M.      319 333
Foster’s theorem      318
Four colour theorem      172
Four-group      172
Fox, R, H.      292
Fractional independence number      169
Frankl, P.      133 144
Frieze, A.M.      252 334
Frobenius, R G.      278
Fulkersoti, D.R.      67 91 101 166
Function, Ackerman      200
Function, Hales — Jewett      200
Function, Shelah’s      201
Function, van der Waerden      199
Fundamental algorithm      86
Fundamental cocycle, vector      53
Fundamental cut      53
Fundamental cut, vector      53
Fundamental cycle      53
Fundamental cycle, vector      53
Fundamental theorem of extremal graph theory      104 120
Furedi, Z.      143
Furstenberg, H.      205
Fuse      149
Fusing      336
Gale, D.      68 85 102
Gallai, T.      101 165 173 178
Galvin, F      163 178 182 205 214
Galvin’s theorem      164
Gasparian, G.S.      169 178
Genus      155
Gessel, L M.      293
Giant component      24 ]
girth      104
Godsil, C.D.      293
Gordon, C.McA.      376 378
Grading      30
Graham, R.L.      144 179 196 197 207 213 266
Graph      1
Graph of a group      254
Graph, acyclic      6
Graph, balanced      228
Graph, bipartite      6
Graph, block-cutvertex      74
Graph, Brinkman      175
Graph, complete      3
Graph, complete r-partite      7
Graph, conductance of      321
Graph, connected      6 73
Graph, cubic      4
Graph, diameter of      10
Graph, directed      8
Graph, disconnected      73
Graph, dual      372
Graph, edge-transitive      291
Graph, empty      3
Graph, Eulerian      16 19
Graph, Grotzsch      170
Graph, Hamiltonian      14
Graph, Heawood      8
Graph, highly regular      272
Graph, homeomorphic      21
Graph, I-transitive      291
Graph, incidence      7
Graph, interval      175
Graph, k-connected      73
Graph, k-critical      173

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