Perfect graphs
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
John Wiley & Sons
2001
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| Schriftenreihe: | Wiley-Interscience Series in Discrete Mathematics and Optimization
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| 245 | 1 | 0 | |a Perfect graphs |c edited by Jorge L. Ramírez Alfonsín, University of Bonn, Germany, Bruce A. Reed, CNRS, Paris, France |
| 264 | 1 | |a Chichester [u.a.] |b John Wiley & Sons |c 2001 | |
| 300 | |a XXII, 362 Seiten |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley-Interscience Series in Discrete Mathematics and Optimization | |
| 650 | 4 | |a Graphes parfaits | |
| 650 | 4 | |a Perfect graphs | |
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| 700 | 1 | |a Ramírez-Alfonsín, Jorge L. |4 edt | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 055f 2001 A 32938 |
|---|---|
| DE-BY-TUM_katkey | 1371663 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020123484 |
| _version_ | 1820814193533648896 |
| adam_text | PERFECT GRAPHS EDITED BY JORGE L. RAMIREZ ALFONSM UNIVERSITY OF BONN,
GERMANY BRUCE A. REED CNRS, PARIS, FRANCE JOHN WILEY & SONS, LTD
CHICHESTER * NEW YORK * WEINHEIM * BRISBANE * SINGAPORE * TORONTO
CONTENTS LIST OF CONTRIBUTORS XIII PREFACE XV ACKNOWLEDGEMENTS XXI 1
ORIGINS AND GENESIS C. BERGE AND J.L. RAMIREZ ALFONSIN 1 1.1 PERFECTION
1 1.2 COMMUNICATION THEORY 1 1.3 THE PERFECT GRAPH CONJECTURE 3 1.4
SHANNON S CAPACITY 7 1.5 TRANSLATION OF THE HALLE-WITTENBERG PROCEEDINGS
7 1.6 INDIAN REPORT 10 REFERENCES 11 2 FROM CONJECTURE TO THEOREM BRUCE
A. REED 13 2.1 GALLAI S GRAPHS 14 2.2 THE PERFECT GRAPH THEOREM 16 2.3
SOME POLYHEDRAL CONSEQUENCES 18 2.4 A STRONGER THEOREM 22 REFERENCES 23
3 A TRANSLATION OF GALLAI S PAPER: TRANSITIV ORIENTIERBARE GRAPHEN
FREDERIC MAFFRAY AND MYRIAM PREISSMANN 25 TRANSLATORS FOREWORD 25 3.1
INTRODUCTION AND RESULTS 26 3.2 THE PROOFS OF THEOREMS (3.1.2), (3.1.5)
AND (3.1.6) 34 3.3 THE PROOFS OF (3.1.8) AND (3.1.9) 38 3.4 THE PROOF OF
(3.1.16) 40 3.5 THE PROOF OF (3.1.17) 44 3.6 DETERMINATION OF ALL
IRREDUCIBLE GRAPHS 47 3.7 DETERMINATION OF THE IRREDUCIBLE GRAPHS 56
REFERENCES 65 VLLL CONTENTS 4 EVEN PAIRS HAZEL EVERETT, CELINA M. H. DE
FIGUEIREDO, CLAUDIA LINHARES SALES, FREDERIC MAFFRAY, OSCAR PORTO AND
BRUCE A. REED 67 4.1 INTRODUCTION 67 4.2 EVEN PAIRS AND PERFECT GRAPHS
70 4.3 PERFECTLY CONTRACTILE GRAPHS 72 4.3.1 WEAKLY TRIANGULATED GRAPHS
72 4.3.2 MEYNIEL GRAPHS 73 4.3.3 PERFECTLY ORDERABLE GRAPHS 75 4.3.4
OTHER CLASSES OF PERFECTLY CONTRACTILE GRAPHS 77 4.3.5 GRAPHS THAT MIGHT
BE PERFECTLY CONTRACTILE 78 4.3.6 FORBIDDEN SUBGRAPHS IN PERFECTLY
CONTRACTILE GRAPHS 78 4.4 QUASI-PARITY GRAPHS 80 4.4.1 CHARACTERIZATION
OF QP AND SQP GRAPHS 82 4.5 RECENT PROGRESS 83 4.5.1 PLANAR GRAPHS 84
4.5.2 CLAW-FREE GRAPHS 85 4.5.3 BULL-FREE GRAPHS 86 4.5.4 DIAMOND-FREE
GRAPHS 87 4.6 ODD PAIRS 88 REFERENCES 89 5 THE PJ-STRUCTURE OF PERFECT
GRAPHS STEFAN HOUGARDY 93 5.1 INTRODUCTION 93 5.2 P 4 -STRUCTURE:
BASICS, ISOMORPHISMS AND RECOGNITION 94 5.3 MODULES, /I-SETS, SPLIT
GRAPHS AND UNIQUE PJ-STRUCTURE 96 5.4 THE SEMI-STRONG PERFECT GRAPH
THEOREM 101 5.5 THE STRUCTURE OF THE PT-ISOMORPHISM CLASSES 102 5.6
RECOGNIZING P 4 -STRUCTURE 105 5.7 THE PI-STRUCTURE OF MINIMALLY
IMPERFECT GRAPHS 106 5.8 THE PARTNER STRUCTURE AND OTHER GENERALIZATIONS
107 5.9 **-STRUCTURE 108 REFERENCES 110 6 FORBIDDING HOLES AND ANTIHOLES
RYAN HAYWARD AND BRUCE A. REED 113 6.1 INTRODUCTION 113 6.2 GRAPHS WITH
NO HOLES 114 6.3 GRAPHS WITH NO DISCS 116 6.4 GRAPHS WITH NO LONG HOLES
120 6.5 BALANCED MATRICES 121 6.6 BIPARTITE GRAPHS WITH NO HOLE OF
LENGTH 4FC + 2 122 6.6.1 SOME PRELIMINARY REMARKS 124 6.6.2 CLEAN HOLES
125 6.6.3 A RECOGNITION ALGORITHM 126 6.6.4 A FRESH LOOK AT CLEANLINESS
127 6.6.5 RECOGNIZING BALANCEABLE GRAPHS 129 CONTENTS IX 6.7 GRAPHS
WITHOUT EVEN HOLES 130 6.7.1 THE DECOMPOSITION THEOREM 131 6.8
/^-PERFECT GRAPHS 132 6.9 GRAPHS WITHOUT ODD HOLES 133 REFERENCES 135 7
PERFECTLY ORDERABLE GRAPHS: A SURVEY CHINH T. HOAENG 139 7.1 INTRODUCTION
139 7.2 CLASSICAL GRAPHS 140 7.2.1 TRIANGULATED GRAPHS 141 7.2.2 CHORDAL
BIPARTITE GRAPHS AND GAMMA-FREE MATRICES 141 7.2.3 COMPARABILITY GRAPHS
141 7.2.4 INTERVAL GRAPHS 142 7.3 MINIMAL NONPERFECTLY ORDERABLE GRAPHS
142 7.4 ORIENTATIONS 144 7.4.1 SIX CLASSES OF PERFECTLY ORDERABLE GRAPHS
144 7.4.2 OPPOSITION ORIENTATION 146 7.5 GENERALIZATIONS OF TRIANGULATED
GRAPHS 147 7.5.1 QUASI-TRIANGULATED GRAPHS 147 7.5.2 BRITTLE GRAPHS 148
7.5.3 QUASI-BRITTLE GRAPHS 149 7.5.4 C-ORIENTATION 149 7.6
GENERALIZATIONS OF COMPLEMENTS OF CHORDAL BIPARTITE GRAPHS 149 7.6.1
CLAW-FREE GRAPHS 149 7.6.2 P 5 -FREE WEAKLY TRIANGULATED GRAPHS 150
7.6.3 BULL-FREE PERFECTLY ORDERABLE GRAPHS 151 7.6.4 D-GRAPHS 151 7.7
OTHER CLASSES OF PERFECTLY ORDERABLE GRAPHS 152 7.7.1 COMPLEMENTS OF
TOLERANCE GRAPHS 152 7.7.2 STRONGLY PERFECTLY ORDERABLE GRAPHS 152 7.7.3
CHARMING GRAPHS 153 7.7.4 NICE GRAPHS 153 7.7.5 BIPARTABLE GRAPHS 153
7.7.6 INTERSECTION AND UNION OF TWO THRESHOLD GRAPHS 153 7.7.7 P 4
COMPOSITION 156 7.8 VERTEX ORDERINGS 156 7.8.1 LEXICOGRAPHIC
BREADTH-FIRST SEARCH 157 7.8.2 MAXIMAL CARDINALITY SEARCH 158 7.8.3
ORDERS BY DEGREES 158 7.9 GENERALIZATIONS OF PERFECTLY ORDERABLE GRAPHS
159 7.9.1 QUASI-PERFECTLY ORDERABLE GRAPHS 160 7.9.2 PROPERLY ORDERABLE
GRAPHS 160 7.9.3 PERFECTLY ORIENTABLE GRAPHS 161 7.10 OPTIMIZING
PERFECTLY ORDERED GRAPHS 161 REFERENCES 163 X CONTENTS 8 CUTSETS IN
PERFECT AND MINIMAL IMPERFECT GRAPHS IRENA RUSU 167 8.1 INTRODUCTION 167
8.2 HOW DID IT START? 168 8.3 MAIN RESULTS ON MINIMAL IMPERFECT GRAPHS
169 8.4 APPLICATIONS: STAR CUTSETS 172 8.5 APPLICATIONS: CLIQUE AND
MULTIPARTITE CUTSETS 174 8.6 APPLICATIONS: STABLE CUTSETS 176 8.7 TWO
(RESOLVED) CONJECTURES 178 8.8 THE CONNECTIVITY OF MINIMAL IMPERFECT
GRAPHS 179 8.9 SOME (MORE) PROBLEMS 181 REFERENCES 181 9 SOME ASPECTS OF
MINIMAL IMPERFECT GRAPHS MYRIAM PREISSMANN AND ANDRDS SEBO 185 9.1
INTRODUCTION 185 9.1.1 DEFINITIONS AND NOTATION 186 9.1.2
CLASSIFICATIONS OF THE RESULTS 188 9.1.3 POLYHEDRA 189 9.1.4 TESTING
IMPERFECTNESS AND PARTITIONABILITY 189 9.2 IMPERFECT AND PARTITIONABLE
GRAPHS 191 9.2.1 BASIC PROPERTIES 191 9.2.2 SMALL CERTIFICATE FOR
IMPERFECTNESS 193 9.2.3 SMALL CERTIFICATES FOR PARTITIONABLE GRAPHS 194
9.3 PROPERTIES 195 9.3.1 PARTITIONABLE AND MINIMAL IMPERFECT GRAPHS 195
9.3.2 GENUINE PROPERTIES 197 9.4 CONSTRUCTIONS 207 9.4.1 GENERALITIES
207 9.4.2 PARTITIONABLE GRAPHS WITH CIRCULAR SYMMETRY 209 9.4.3 ADDING A
CRITICAL CLIQUE 210 REFERENCES 212 10 GRAPH IMPERFECTION AND CHANNEL
ASSIGNMENT COLIN MCDIARMID 215 10.1 INTRODUCTION 215 10.2 THE
IMPERFECTION RATIO 217 10.3 ALTERNATIVE DEFINITIONS 219 10.4 FURTHER
RESULTS AND QUESTIONS 220 10.4.1 LIST COLOURING 220 10.4.2 TRIANGLE-FREE
PLANAR GRAPHS 221 10.4.3 IMPERFECTION AND ODD HOLES 221 10.4.4 DILATION
RATIO 222 10.4.5 GRAPH ENTROPY 223 10.4.6 RANDOM GRAPHS 224 10.4.7
EXTREMAL BEHAVIOUR 225 10.4.8 HARDNESS 225 10.4.9 LEXICOGRAPHIC PRODUCTS
225 10.4.10 VALUES OF IMP(G) 225 CONTENTS XI 10.4.11 HOLES AND ANTIHOLES
226 10.4.12 BINARY IMPERFECTION RATIO 226 10.4.13 CIRCULAR ARC GRAPHS
226 10.4.14 UNIT DISC GRAPHS 227 10.5 BACKGROUND ON CHANNEL ASSIGNMENT
227 REFERENCES 229 11 A GENTLE INTRODUCTION TO SEMI-DEFINITE PROGRAMMING
BRUCE A. REED 233 11.1 INTRODUCTION 233 11.2 THE ELLIPSOID METHOD 235
11.2.1 HOW THE ALGORITHM WORKS 237 11.2.2 SOLVING LPS 239 11.3 SOLVING
SEMI-DEFINITE PROGRAMS 241 11.4 RANDOMIZED ROUNDING AND DERANDOMIZATION
244 11.4.1 THE METHOD OF CONDITIONAL EXPECTATION FOR MAXSAT 245 11.4.2
RANDOMIZED ROUNDING 246 11.4.3 A COMBINED APPROACH 247 11.4.4 RANDOM
PROJECTION 248 11.5 APPROXIMATING MAXCUT 248 11.6 APPROXIMATING
BANDWIDTH 250 11.6.1 THE FIRST ALGORITHM 250 11.6.2 A MORE SOPHISTICATED
ALGORITHM 252 11.7 GRAPH COLOURING 252 11.7.1 COLOURING PERFECT GRAPHS
252 11.7.2 COLOURING 3-COLOURABLE GRAPHS 254 11.8 THE THETA BODY 256
REFERENCES 258 12 THE THETA BODY AND IMPERFECTION F.B. SHEPHERD 261 12.1
BACKGROUND AND OVERVIEW 261 12.1.1 PERFECTION AND INTEGER PROGRAMMING
261 12.1.2 IMPERFECTION AND PARTITIONABILITY 262 12.1.3 OVERVIEW 263
12.1.4 PARTITIONABILITY AND BRANCH AND CUT METHODS FOR PACKING PROBLEMS
266 12.2 OPTIMIZATION, CONVEXITY AND GEOMETRY 267 12.2.1 CONVEXITY AND
ENCODING CONVENTIONS 268 12.2.2 OPTIMIZATION OVER A CONVEX BODY:
CONSEQUENCES OF THE ELLIPSOID METHOD 269 12.2.3 THE DISCOVERY PROBLEM
270 12.3 THE THETA BODY 272 12.3.1 THREE CONVEX BODIES 272 12.3.2 A
SEMI-DEFINITE FORMULATION 273 12.3.3 ALGORITHMS FOR THE THETA BODY 275
12.3.4 ADDITIVE GAP GUARANTEES AND THE PROTRUSION OF THE THETA BODY 276
XII CONTENTS 12.4 PARTITIONABLE GRAPHS 280 12.4.1 A CHARACTERIZATION 280
12.4.2 A RECOGNITION ALGORITHM 283 12.5 PERFECT GRAPH CHARACTERIZATIONS
AND A CONTINUOUS PERFECT GRAPH CONJECTURE 285 REFERENCES 289 13 PERFECT
GRAPHS AND GRAPH ENTROPY GABOR SIMONYI 293 13.1 INTRODUCTION 293 13.2
THE INFORMATION-THEORETIC INTERPRETATION 295 13.3 SOME BASIC PROPERTIES
297 13.3.1 MONOTONICITY 297 13.3.2 SUB-ADDITIVITY 298 13.3.3 ADDITIVITY
OF SUBSTITUTION 298 13.4 STRUCTURAL THEOREMS: RELATION TO PERFECTNESS
300 13.4.1 ADDITIVITY FOR COMPLEMENTARY PAIRS 300 13.4.2 IMPERFECTION
RATIO 302 13.4.3 ADDITIVITY FOR ARBITRARY PAIRS 304 13.4.4 SUB- AND
SUPERMODULAR PAIRS 306 13.4.5 WEAK ADDITIVITY AND NORMALITY 307 13.5
APPLICATIONS 309 13.5.1 KAHN AND KIM S APPLICATION FOR SORTING 309
13.5.2 ABOUT OTHER APPLICATIONS 310 13.6 GENERALIZATIONS 312 13.6.1
HYPERGRAPH ENTROPY 312 13.6.2 ADDITIVITY FOR COMPLEMENTARY UNIFORM
HYPERGRAPHS 312 13.6.3 ENTROPY OF CONVEX CORNERS 315 13.6.4 JOB
SCHEDULING APPLICATION 315 13.7 GRAPH CAPACITIES AND OTHER RELATED
FUNCTIONALS 316 13.7.1 SHANNON CAPACITY 316 13.7.2 SPERNER CAPACITY 319
13.7.3 PROBABILISTIC LOVAESZ FUNCTION 321 13.7.4 CO-ENTROPY 323
REFERENCES 325 14 A BIBLIOGRAPHY ON PERFECT GRAPHS VASEK CHVDTAL 329
INDEX 359
|
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| id | DE-604.BV014105036 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T15:47:34Z |
| institution | BVB |
| isbn | 0471489700 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009662737 |
| oclc_num | 46640717 |
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| owner | DE-703 DE-91G DE-BY-TUM DE-83 DE-11 DE-188 |
| owner_facet | DE-703 DE-91G DE-BY-TUM DE-83 DE-11 DE-188 |
| physical | XXII, 362 Seiten graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | John Wiley & Sons |
| record_format | marc |
| series2 | Wiley-Interscience Series in Discrete Mathematics and Optimization |
| spellingShingle | Perfect graphs Graphes parfaits Perfect graphs Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4113782-6 |
| title | Perfect graphs |
| title_auth | Perfect graphs |
| title_exact_search | Perfect graphs |
| title_full | Perfect graphs edited by Jorge L. Ramírez Alfonsín, University of Bonn, Germany, Bruce A. Reed, CNRS, Paris, France |
| title_fullStr | Perfect graphs edited by Jorge L. Ramírez Alfonsín, University of Bonn, Germany, Bruce A. Reed, CNRS, Paris, France |
| title_full_unstemmed | Perfect graphs edited by Jorge L. Ramírez Alfonsín, University of Bonn, Germany, Bruce A. Reed, CNRS, Paris, France |
| title_short | Perfect graphs |
| title_sort | perfect graphs |
| topic | Graphes parfaits Perfect graphs Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Graphes parfaits Perfect graphs Graphentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009662737&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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