Here - Combinatorial algorithms and algorithmic graph theory

More documents

Recommendations

Info

ii Dankwoord en minder wetenschappelijke discussies gevoerd heb. During my PhD I have also had a wonderful research stay at the Australian National University in Canberra. I was very warmly welcomed there and I immediately felt at home. Brendan, Fateme, Leanne, Miriam, Mirka, Mohammadreza and Pascal, thanks a lot for the great time you gave me in Australia and I hope I will be seeing you again sooner or later. During the last year of my PhD I also had the honour of collaborating with Professor Staszek Radziszowski on Ramsey numbers. I really learned a lot from him. During this period we exchanged hundreds of emails and I was very happy to meet Staszek in person at two conferences. I also really enjoyed my research stay with him in Rochester where he took great care of me. So Staszek, really thanks a lot for everything! Tenslotte wil ik ook het Fonds Wetenschappelijk Onderzoek Vlaanderen bedanken voor de vele kansen die ze me geboden hebben door me deze beurs te geven. Ik heb tijdens mijn doctoraat ook veel gebruikgemaakt van de STEVIN supercomputer van de Universiteit Gent. Daarom ben ik het STEVIN-team heel dankbaar voor hun uitstekende ondersteuning. Jan Goedgebeur mei 2013
Contents Summary vii 1 Introduction 1 1.1 Definitions and preliminaries . . . . . . . . . . . . . . . . . . . . . 3 1.2 Exhaustive generation . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Isomorphism-free generation . . . . . . . . . . . . . . . . . . . . . . 6 2 Generation of cubic graphs 11 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 The generation algorithm . . . . . . . . . . . . . . . . . . . . . . . 13 2.3 Generation of prime graphs . . . . . . . . . . . . . . . . . . . . . . 14 2.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.2 Isomorphism rejection . . . . . . . . . . . . . . . . . . . . . 16 2.3.3 Determining possible expansions . . . . . . . . . . . . . . . 23 2.3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4 Generation of graphs with reducible triangles . . . . . . . . . . . . 28 2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4.2 Construction . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.4.3 Optimisations . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.5 Generation of non-prime graphs without reducible triangles . . . . 34 2.5.1 Isomorphism rejection . . . . . . . . . . . . . . . . . . . . . 34 2.5.2 Determining possible expansions . . . . . . . . . . . . . . . 37 2.5.3 Optimisations . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.6 Generation of graphs with girth at least 4 or 5 . . . . . . . . . . . 43 2.6.1 Graphs with girth at least 4 . . . . . . . . . . . . . . . . . . 43 iii
Page 1: Ghent University Faculty of Science
Page 5: Dankwoord Deze thesis zou er zeker
Page 9 and 10: Contents v 5.2.1 Introduction . . .
Page 11 and 12: Summary In this thesis we develop e
Page 13 and 14: Summary ix represent carbon atoms.
Page 15 and 16: Chapter 1 Introduction A graph is a
Page 17 and 18: 1.1. Definitions and preliminaries
Page 19 and 20: 1.2. Exhaustive generation 5 A k-fa
Page 21 and 22: 1.3. Isomorphism-free generation 7
Page 23 and 24: 1.3. Isomorphism-free generation 9
Page 25 and 26: Chapter 2 Generation of cubic graph
Page 27 and 28: 2.2. The generation algorithm 13 of
Page 29 and 30: 2.3. Generation of prime graphs 15
Page 43 and 44: 2.4. Generation of graphs with redu
Page 49 and 50: 2.5. Generation of non-prime graphs
Page 57 and 58:
2.6. Generation of graphs with girt
Page 59 and 60:
2.6. Generation of graphs with girt
Page 61 and 62:
2.7. Generation of graphs with conn
Page 63 and 64:
2.7. Generation of graphs with conn
Page 65 and 66:
2.9. Closing remarks 51 strongly on
Page 67 and 68:
2.9. Closing remarks 53 All connect
Page 69 and 70:
Chapter 3 Generation of snarks In t
Page 71 and 72:
3.1. Introduction 57 smallest snark
Page 73 and 74:
3.3. The generation algorithm 59 As
Page 75 and 76:
3.4. Optimisations 61 At first sigh
Page 77 and 78:
3.4. Optimisations 63 the non-isomo
Page 79 and 80:
3.5 Testing and results 3.5. Testin
Page 81 and 82:
3.5. Testing and results 67 Order 1
Page 83 and 84:
3.6. Closing remarks 69 Figure 3.2:
Page 85 and 86:
3.6. Closing remarks 71 snarks of s
Page 87 and 88:
Chapter 4 Generation of fullerenes
Page 89 and 90:
4.1. Introduction 75 However, Whitn
Page 91 and 92:
4.1. Introduction 77 incomplete in
Page 93 and 94:
4.2. Generation of fullerenes 79 or
Page 95 and 96:
4.2. Generation of fullerenes 81 C
Page 97 and 98:
4.2. Generation of fullerenes 83 00
Page 99 and 100:
4.2. Generation of fullerenes 85 wi
Page 101 and 102:
4.2. Generation of fullerenes 87 We
Page 103 and 104:
4.2. Generation of fullerenes 89 e
Page 105 and 106:
4.3. Generation of IPR fullerenes 9
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
4.4. Testing and results 113 adding
Page 129 and 130:
4.4. Testing and results 115 number
Page 131 and 132:
4.4. Testing and results 117 nv nf
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
4.4. Testing and results 123 Figure
Page 139 and 140:
4.5. Closing remarks 125 Figure 4.3
Page 141 and 142:
Chapter 5 Ramsey numbers In the fir
Page 143 and 144:
5.2. Generalised triangle Ramsey nu
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
5.3. Classical triangle Ramsey numb
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
Page 193 and 194:
Page 195 and 196:
Page 197 and 198:
Appendix A Notation 183
Page 199 and 200:
Appendix B Ramsey numbers of connec
Page 201 and 202:
187 and contains one of the graphs:
Page 203 and 204:
Appendix C Number of Ramsey graphs
Page 205 and 206:
191 edges number of vertices n e 19
Page 207 and 208:
193 edges number of vertices n e 29
Page 209 and 210:
Bibliography [1] E. Albertazzi, C.
Page 211 and 212:
Bibliography 197 [23] G. Brinkmann
Page 213 and 214:
Bibliography 199 [48] G. Exoo. On t
Page 215 and 216:
Bibliography 201 [74] C. Justus. Tr
Page 217 and 218:
Bibliography 203 [101] S.P. Radzisz
Page 219 and 220:
Bibliography 205 [126] C.Q. Zhang.
Page 221 and 222:
Nederlandstalige samenvatting In de
Page 223 and 224:
Nederlandstalige samenvatting 209 v
Page 225 and 226:
List of Figures 1.1 The basic edge
Page 227 and 228:
List of Figures 213 4.13 An L 2 exp
Page 229 and 230:
List of Tables 2.1 Number of prime
Page 231 and 232:
List of Tables 217 5.2 Counts and g
Page 233 and 234:
Index 219 edge-cut, 4 embedding, 74
show all

Here - Combinatorial algorithms and algorithmic graph theory

Create successful ePaper yourself

Delete template?

Save as template?