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Toplcs in Structural Graph Theory2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

Lowell W. Beineke ; Robin J. Wilson ; Ortrud R. Oellermann 著
出版社： Cambridge University Press
ISBN：0521802314
出版时间：2013
标注页数：328页
文件大小：40MB
文件页数：343页
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图书目录

Preliminaries&LOWELL W.BEINEKE and ROBIN J.WILSON1

1.Graph theory1

2.Connectivity8

3.Flows in networks10

1 Menger’s theorem&ORTRUD R.OELLERMANN13

1.Introduction13

2.Vertex-connectivity14

3.Edge-connectivity18

4.Mixed connectivity19

5.Average connectivity22

6.Menger results for paths of bounded length28

7.Connectivity of sets30

8.Connecting with trees32

2 Maximally connected graphs&DIRK MEIERLING and LUTZ VOLKMANN40

1.Introduction40

2.Maximally edge-connected graphs41

3.Maximally edge-connected digraphs46

4.Maximally locally edge-connected graphs and digraphs48

5.Maximally connected and maximally locally connected graphs and digraphs50

6.Restricted edge-connectivity54

7.Conditional vertex-connectivity and edge-connectivity58

3 Minimal connectivity&MATTHIAS KRIESELL71

1.Introduction71

2.Edge-deletion73

3.Vertex-deletion74

4.Edge-contraction79

5.Generalized criticality81

6.Reduction methods82

7.Subgraph-deletion88

8.Partitions under connectivity constraints91

9.Line graphs94

4 Contractions of k-connected graphs&KIYOSHI ANDO100

1.Introduction100

2.Contractible edges in 3-connected graphs101

3.Contractible edges in 4-connected graphs102

4.Contractible edges in k-connected graphs103

5.Contraction-critical 5-connected graphs106

6.Local structure and contractible edges109

7.Concluding remarks111

5 Connectivity and cycles&R.J.FAUDREE114

1.Introduction114

2.Generalizations of classical results115

3.Relative lengths of paths and cycles117

4.Regular graphs119

5.Bipartite graphs122

6.Claw-free graphs123

7.Planar graphs128

8.The Chvatal-Erdos condition131

9.Ordered graphs132

10.Numbers of cycles134

6 H-linked graphs&MICHAEL FERRARA and RONALD J.GOULD141

1.Introduction141

2.k-linked graphs143

3.Weak linkage149

4.Digraphs150

5.Modulo and parity linkage152

6.Disjoint connected subgraphs154

7.The disjoint paths problem154

8.H-linked graphs155

9.H-extendible graphs159

7 Tree-width and graph minors&DIETER RAUTENBACH and BRUCE REED165

1.Introduction165

2.Subtree intersection representation166

3.Tree decomposition and tree-width168

4.Tree decompositions decompose173

5.Excluding planar minors174

6.Wagner’s conjecture175

7.The dual of tree-width176

8.A canonical tree decomposition178

9.Wagner’s conjecture for arbitrary graphs180

10.Efficient characterization of H-minor-free graphs181

8 Toughness and binding numbers&IAN ANDERSON185

1.Introduction185

2.Toughness and connectivity187

3.Toughness and cycles188

4.Toughness and k-factors191

5.Binding number194

6.Binding number and k-factors196

7.Binding numbers and cycles198

8.Other measures of vulnerability198

9 Graph fragmentability&KEITH EDWARDS and GRAHAM FARR203

1.Introduction203

2.Values and bounds for fragmentability206

3.Reduction and separation207

4.Bounded degree classes208

5.Planarization210

6.Applications214

7.Monochromatic components215

8.Open problems216

10 The phase transition in random graphs&BELA BOLLOBAS and OLIVER RIORDAN219

1.Introduction219

2.The Erdos-Renyi theorem：the double jump223

3.Correction：no double jump225

4.The phase transition - simple results227

5.Exploring components238

6.The phase transition - finer results240

7.The young giant243

8.Final words247

11 Network reliability and synthesis&F.T.BOESCH，A.SATYANARAYANA and C.L.SUFFEL251

1.Introduction251

2.Domination in digraphs252

3.Coherent systems and domination in graphs255

4.Computational complexity of reliability260

5.Synthesis of reliable networks260

6.Other measures of vulnerability263

12 Connectivity algorithms&ABDOL-HOSSEIN ESFAHANIAN268

1.Introduction268

2.Computing the edge-connectivity269

3.Computing the arc-connectivity274

4.Computing the vertex-connectivity275

5.Concluding remarks279

13 Using graphs to find the best block designs&R.A.BAILEY and PETER J.CAMERON282

1.What makes a block design good？283

2.Graphs from block designs284

3.Statistical issues288

4.Highly patterned block designs292

5.D-optimality293

6.A-optimality294

7.E-optimality302

8.Some history304

9.Block size 2306

10.Low average replication311

11.Further reading314

Notes on contributors318

Index323