Partial representation extension and simultaneous representation of intersection graphs:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Hochschulschrift/Dissertation Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Passau
2024
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| Schlagwörter: | |
| Links: | https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/1520 https://nbn-resolving.de/urn:nbn:de:bvb:739-opus4-15201 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035488635&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | ix, 208 Seiten Illustrationen |
Internformat
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Datensatz im Suchindex
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Contents Abstract Acknowledgments Contents Hi v vH Introduction 1.1 Partial Representation Extension. 1.2 Simultaneous Representation. 1.3 Overview and Results. 1 2 4 6 2 Preliminaries 2.1 Intersection Graphs and Problems. 2.2 PQ-Trees. . . 13 13 15 1 I Partial Representation Extension 17 3 Partial Representation Extension for Circular-ArcGraphs 3.1 Introduction. 3.2 Preliminaries. 3.3 NP-Completeness Results. 3.3.1 NP-Completeness for UCA. 3.3.2 NP-Completeness for CA and HCA . 3.4 Normal Proper Helly Circular-Arc Graphs . 3.5 Proper Helly Circular-Arc Graphs. 3.6 Normal Helly Circular-Arc Graphs. 3.7 Helly Circular-Arc Graphs . 3.8 Conclusion. 21 21 23 25 26 27 29 31 35 42 45 4 Partial Representation Extension for Circle Graphs 4.1 Introduction. 4.2
Preliminaries. 4.2.1 Circle Graphs and Chord Diagrams. 47 47 49 49 vii
5 4.2.2 Splits and Split Trees. 4.3 Compact Representation of all Chord Diagrams. 4.3.1 Configurations of Split Trees . 4.3.2 Configurations of Canonical Split Trees. 4.4 Partial Representation Extension. 4.4.1 Representation Test in Restricted Split Trees. 4.4.2 The Actual Extension. 4.5 Conclusion. 50 53 53 58 62 65 69 70 Partial Transitive Orientation Extension 5.1 Preliminaries. 5.2 Modular Decompositions. 5.3 Transitive Orientation Extension. 5.4 Permutation Graphs. 5.5 Circular Permutation Graphs. 5.6 Conclusion. 71 71 72 76 77 80 82 11 Simultaneous Representation 6 7 viii Sunflower Simultaneous Interval Graphs 6.1 Simultaneous Clique Orderings . 6.2 Operations on PQ-Trees. 6.3
Algorithm. 6.3.1 Polynomial-Time Algorithm. 98 6.3.2 Linear-Time Algorithm. 101 6.4 Conclusion. Simultaneous Proper and Unit IntervalGraphs 7.1 Preliminaries. 7.2 Sunflower Proper IntervalGraphs. 7.2.1 Characterization. 109 7.2.2 A Simple Recognition Algorithm. 112 7.2.3 Combinatorial Description. 113 7.3 Sunflower UnitInterval Graphs . 7.3.1 Simultaneous Enumerations of Sunflower Unit Interval Graphs. 7.3.2 Recognizing Sunflower Unit IntervalGraphs in Polynomial Time. 83 89 90 92 96 104 107 107 109 116 116 127
Recognizing Sunflower Unit Interval Graphs in O(| V| · |£|) Time. 128 NP-Completeness for the Non-Sunflower Case. Conclusion. 7.3.3 7.4 7.5 8 Sunflower Circle Graphs 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 9 Constrained Split Trees. Turning and Reversing Constraint Trees . Cleanup . Testing and Normalization. Exposing a Set of Splits. The Algorithm. NP-Completeness for Non-Connected Shared Graph with к = 3 . Conclusion. Simultaneous Transitive Orientations 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 Restricted Modular Decompositions. The Constrained Modular Decomposition. 9.2.1 Constraints for Prime Nodes. 9.2.2 Constraints for Complete Nodes . 9.2.3 Correctness.
Algorithm. Sunflower Permutation Graphs. Sunflower Circular Permutation Graphs. Sunflower Function Graphs. NP-Completeness for the Non-Sunflower Case. Conclusion. 10 Conclusions Outlook 10.1 Summary. 10.1.1 Partial Representation Extension. 10.1.2 Simultaneous Representation. 10.2 Outlook. 10.2.1 Sunflower Alternatives. Bibliography 132 134 137 137 138 141 145 149 160 163 164 167 167 169 169 171 175 178 179 181 183 184 187 189 189 189 191 192 193 197 ix |
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| spellingShingle | Stumpf, Peter Frederik ca. 20./21. Jh Partial representation extension and simultaneous representation of intersection graphs Geometrische Graphentheorie (DE-588)1201437083 gnd |
| subject_GND | (DE-588)1201437083 (DE-588)4113937-9 |
| title | Partial representation extension and simultaneous representation of intersection graphs |
| title_auth | Partial representation extension and simultaneous representation of intersection graphs |
| title_exact_search | Partial representation extension and simultaneous representation of intersection graphs |
| title_full | Partial representation extension and simultaneous representation of intersection graphs Peter Frederik Stumpf |
| title_fullStr | Partial representation extension and simultaneous representation of intersection graphs Peter Frederik Stumpf |
| title_full_unstemmed | Partial representation extension and simultaneous representation of intersection graphs Peter Frederik Stumpf |
| title_short | Partial representation extension and simultaneous representation of intersection graphs |
| title_sort | partial representation extension and simultaneous representation of intersection graphs |
| topic | Geometrische Graphentheorie (DE-588)1201437083 gnd |
| topic_facet | Geometrische Graphentheorie Hochschulschrift |
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