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Diestel R. — Graph Theory
Diestel R. — Graph Theory



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Название: Graph Theory

Автор: Diestel R.

Аннотация:

This book is a concise, yet carefully written, introduction to modern graph theory, covering all its recent developments. It 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. This second edition extends the first in two ways. It offers a thoroughly revised and updated chapter on graph minors, which now includes full new proofs of two of the central Robertson-Seymor theorems (as well as a detailed sketch of the entire proof of their celebrated Graph Minor Theorem). Second, there is now a section of hints for all the exercises, to enhance their value for bith individual study and classroom use.


Язык: en

Рубрика: Математика/Алгебра/Комбинаторика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second edition

Год издания: 2000

Количество страниц: 312

Добавлена в каталог: 07.12.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Ramsey graph      197
Ramsey numbers      191 193—194 209 210 232
Ramsey theory      189—208
Ramsey theory and connectivity      207—208
Ramsey theory, induced      196—206
Ramsey theory, infinite      192 208 210
Ramsey, F.P      190—193
Ramsey-minimal      196
Random graph      179 194 229—250 231
Random graph, evolution      241
Random graph, infinite      248
Random graph, process      250
Random graph, uniform model      250
Random variable      233
Random variable, indicator r.v.      234 295
Reducible configuration      121
Reed, B.A.      281
Refining a partition      1 155—159
Region      68—70
Region on $S^2$      70
Regular      5 33 226
Regularity graph      161
Regularity graph, inflated, $R_S$      194
Regularity lemma      148 153—164 154 167 210
Renyi, A.      243 249
Richardson, M.      119
Rigid-circuit      see “Chordal”
Riha, S.      228
Robertson, N.      66 121 183 186 257 264 275 281
Rodl, V.      167 194 197 211
Ronyai, L.      167
Root      13
Rooted tree      13 253 278
Rothschild, B.L.      210
Royle, G.F.      28
Rucihski, A.      249
Sanders, D.P.      121
Sarkozy, G.N.      226
Saturated      see “Edge-maximal”
Schelp, R.H.      210
Schoenflies, A.M.      70
Schrijver, A.      145
Schur, I.      209
Scott, A.D.      167 178 209
Second moment      242—247
Self-minor conjecture      280
Separate a graph      10 50 55 56
Separate the plane      68
Separating set      10
Sequential colouring      see “Greedy algorithm”
Series-parallel      185
Set system      see “Hypergraph”
Seymour, P.D.      66 92 121 141 183 186 187 226 257 258 264 275 280 281
Shift-graph      209
Simonovits, M.      166 167 210
Simple basis      85 92—93
Simple graph      26
Simplicial tree-decomposition      261 275 279 281
Sink      125
Six-flow theorem      141
Snark      141
Snark planar      141 145 215
Sos, V.      152 166 167
Source      125
Spanned subgraph      3
Spanning subgraph      3
Spanning trees      13 14
Spanning trees, edge disjoint      58—60
Spanning trees, number of      248
Sparse graphs      147 169—185 194
Spencer, J.H.      210 249
Sperner’s lemma      41
Square of graph      218
Square, Latin      119
Stability number      see “Independence number”
Stable set      3
Standard basis      20
Star      15 166 196
Star, induced      207
Star-shape      287
Steger, A.      117 122
Steinitz, E.      92
Stereographic projection      69
Stone, A.H.      151 160
Straight line segment      68
Strong core      289
Subcontraction      see “Minor”
Subdividing vertex      18
Subdivision      18
Subgraph      3
Subgraph of all large k-connected graphs      207—208
Subgraph of high connectivity      11
Subgraph of large minimum degree      5—6 99 118
Subgraph, forced by edge density      147—164
Subgraph, induced      3
Sum of edge sets      20
Sum of flows      133
Supergraph      3
Symmetric difference      20 29—30 40 53
System of distinct representatives      41
Szabo, T.      167
Szekeres, G.      208 209
Szemeredi, E.      154 170 186 194 226
tail      see “Initial vertex”
Tait, P.G.      121 227—228
Tangle      281
Tarsi, M.      121
ter(e)      23
Terminal vertex      25
Thomas, R.      121 183 208 210 258 280
Thomason, A.G.      66 170 179 186 241
Thomassen, C.      65 92 106 121 179 185 187 228 281 282
Three colour theorem      97
Three-flow conjecture      141
Threshold function      241—247 250
Toft, B.      120 146
Topological isomorphism      76 78 88
Topological minor      17—18
Topological minor $K^4$      182 185 263
Topological minor $K^5$      92 184
Topological minor $K^5$ and $K_{3,3}$      75 80—84
Topological minor $K^5_{_}$      185
Topological minor $K^r$      61 170—178
Topological minor $K_{3,3}$      92 185
Topological minor and planarity      75 80—84 90
Topological minor and WQO of general graphs      278
Topological minor and WQO of trees      253
Topological minor as order relation      18
Topological minor of all large 2-connected graphs      207
Topological minor vs. ordinary minor      18—19 80
Topological minor, forced by average degree      61 170—178
Topological minor, forced by chromatic number      181
Topological minor, forced by girth      178
Topological minor, induced      178
Topological minor, tree (induced)      178
Torso      279
Total chromatic number      119
Total colouring      119
Total colouring, conjecture      119 122
Total value of a flow      126
Touching sets      258
Tournament      227
Transitive graph      41
Travelling salesman problem      227
TREE      12—14
Tree as forced substructure      13 178 185
Tree, cover      61
Tree, normal      13—14 27 139 144 296
Tree, threshold function for      247
Tree, well-quasi-ordering of trees      253—254
Tree-decomposition      186 255—262 278 280—281
Tree-decomposition, induced on minors      256
Tree-decomposition, induced on subgraphs      256
Tree-decomposition, lean      261
Tree-decomposition, obstructions      258—260 264—265 280 281
Tree-decomposition, part of      255
Tree-decomposition, simplicial      261 275 279 281
Tree-decomposition, width of      257
Tree-order      13
Tree-width      257—274
Tree-width and brambles      258—260 278 281
Tree-width and forbidden minors      263—274
Tree-width of a minor      257
Tree-width of a subdivision      278
Tree-width of grid      260 278 281
Tree-width, duality theorem      255—260
Tree-width, obstructions to small      258—260 264—265 280 281
triangle      3
Triangulated      see “Cordal”
Triangulation      see “Plane triangulation”
Trivial graph      2
Trotter, W.T.      194
Turan, graph      149—152 166 292
Turan, P.      150
Turan, theorem      150 195
Tutte polynomial      146
Tutte, flow conjectures      140—141
Tutte, W.T.      35 46 47 58 65 66 86 92 128 131 139 145 146 215 228
tw(G)      255
TX      16
Tychonov, A.N.      210
Unbalanced subgraph      247 249
Uniformity lemma      see “Regularity lemma”
union      3
Unmatched      29
Upper density      166
Urquhart, A.      121
V(G)      2
Valency (degree)      5
Value of a flow      126
Variance      242
Vertex      2
Vertex cut      see “Separating set”
Vertex of a plane graph      70
Vertex space      20
Vertex, colouring      95 98—103
Vertex, cover      30
Vertex-chromatic number      95
Vertex-connectivity      10
Vertex-transitive      41
Vince, A.      249
Vizing, V.G.      103 121 122 289 290 293
Voigt, M.      121
Wagner graph      183 261—262 279
Wagner, K.      84 93 183 184 185 186 281
Walk      9
Walk, alternating      52
Walk, closed      9
Walk, length      9
Well-ordering      294
Well-quasi-ordering      251—282
Welsh, D.J.A.      146
Wheel      46
Wheel theorem      46 65
Whitney, H.      66 80 89
Width of tree-decomposition      257
Winkler, P.      249
xP, Px, xPy, xPyQz, ...      7
xTy, ...      13
xy, $x_1$...$x_k$, ...      2 7
Zykov, A.A.      166
\      70
‘Wagner’s Conjecture’      281
1 2 3 4
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