Extremal graph theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Mineola, NY
Dover Publications
2004
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| Edition: | unabridged republication |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 488 S. Ill. u. graph. Darst. |
| ISBN: | 0486435962 |
Staff View
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Record in the Search Index
| _version_ | 1804132982094561281 |
|---|---|
| adam_text | Contents Preface...............................................................................................................vii Basic Definitions..................................................................................................... xiii Chapter 1 : Connectivity............................................................................................... 1 1. Elementary Properties..................................................................................... 2 2. Menger’s Theorem and its Consequences........................................................ 7 3. The Structure of 2-and З-Connected Graphs..................................... 11 4. Minimally k-Connected Graphs.......................................................................... 17 5. Graphs with Given Maximal Local Connectivity............................................. 29 6. Exercises, Problems and Conjectures........................................................ 45 Chapter 2: Matching............................................................................................. 50 1. Fundamental Matching Theorems................................................................ 52 2. The Number of 1-Factors.................................................................................... 59 3. /-Factors ........... 67 4. Matching in Graphs with Restrictions on the Degrees .... 79 5. Coverings...................................................................................................... 90 6. Exercises, Problems and
Conjectures................................................................ 95 Chapter 3: Cycles..................................................................................................... 102 1. Graphs with Large Minimal Degree and LargeGirth .103 2. Vertex Disjoint Cycles.................................................................................. 110 3. Edge Disjoint Cycles.................................................................................. 119 4. The Circumference........................................................................................... 131 5. Graphs with Cycles of Given Lengths............................................................... 147 6. Exercises, Problems and Conjectures............................................................... 161 Chapter 4: The Diameter.................................................................................. 169 1. 2. 3. 4. 5. Diameter, Maximal Degree and Size............................................................... 170 Diameter and Connectivity......................................................................... 181 Graphs with Large Subgraphs of Small Diameter............................................ 194 Factors of Small Diameter.........................................................................206 Exercises, Problems and Conjectures............................................................... 213 xi
CONTENTS xii Chapter 5: Colourings....................................................................................................... 218 1. General Colouring Theorems........................................................................ 221 2. Critical k-Chromatic Graphs........................................................................ 234 3. Colouring Graphs on Surfaces........................................................................ 243 4. Sparse Graphs of Large Chromatic Number.............................................254 5. Perfect Graphs........................................................................... .263 6. Ramsey Type Theorems.................................................................................. 270 7. Exercises, Problems and Conjectures.............................................................. 280 ........ 292 1. The Number of Complete Subgraphs ......... ..................................................... 293 2. Complete Subgraphs of r-Partite Graphs..................................................... 309 3. The Structure of Graphs................................................................................. 327 4. The Structure of Extremal Graphs without Forbidden Subgraphs . . 339 5. Independent Complete Subgraphs...............................................................351 6. Exercises, Problems and Conjectures............................................................... 359 Chapter 6: Complete Subgraphs Chapter 7 : Topological
Subgraphs.................................................................................. 368 1. Contractions.....................................................................................................369 2. Topological Complete Subgraphs ....... 378 3. Semi-Topological Subgraphs........................................................................ 386 4. Exercises, Problems and Conjectures............................................................... 397 Chapters: Complexity and Packing.................................................................................. 401 1. 2. 3. 4. 5. 6. The Complexity of Graph Properties.............................................................. 402 MonotoneProperties................................................................................. 411 The Main Packing Theorem........................................................................ 418 Packing Graphs of Small Size........................................................................ 425 Applications of Packing Results to Complexity ..... 429 Exercises, Problems and Conjectures.............................................................. 434 References.............................................................................................................. 438 Index of Symbols ............................................................................................ 481 Index of Definitions........................................................ 485
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| any_adam_object | 1 |
| author | Bollobás, Béla 1943- |
| author_GND | (DE-588)109481240 |
| author_facet | Bollobás, Béla 1943- |
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| dewey-full | 511/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.5 |
| dewey-search | 511/.5 |
| dewey-sort | 3511 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | unabridged republication |
| format | Book |
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| id | DE-604.BV019619094 |
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| indexdate | 2024-07-09T20:01:28Z |
| institution | BVB |
| isbn | 0486435962 |
| language | English |
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| physical | XX, 488 S. Ill. u. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Dover Publications |
| record_format | marc |
| spelling | Bollobás, Béla 1943- Verfasser (DE-588)109481240 aut Extremal graph theory unabridged republication Mineola, NY Dover Publications 2004 XX, 488 S. Ill. u. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Teoria dos grafos larpcal Extremal problems (Mathematics) Graph theory Graph (DE-588)4021842-9 gnd rswk-swf Extremalproblem (DE-588)4439315-5 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s DE-604 Graph (DE-588)4021842-9 s 1\p DE-604 Extremalproblem (DE-588)4439315-5 s 2\p DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012948531&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bollobás, Béla 1943- Extremal graph theory Teoria dos grafos larpcal Extremal problems (Mathematics) Graph theory Graph (DE-588)4021842-9 gnd Extremalproblem (DE-588)4439315-5 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4021842-9 (DE-588)4439315-5 (DE-588)4113782-6 |
| title | Extremal graph theory |
| title_auth | Extremal graph theory |
| title_exact_search | Extremal graph theory |
| title_full | Extremal graph theory |
| title_fullStr | Extremal graph theory |
| title_full_unstemmed | Extremal graph theory |
| title_short | Extremal graph theory |
| title_sort | extremal graph theory |
| topic | Teoria dos grafos larpcal Extremal problems (Mathematics) Graph theory Graph (DE-588)4021842-9 gnd Extremalproblem (DE-588)4439315-5 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Teoria dos grafos Extremal problems (Mathematics) Graph theory Graph Extremalproblem Graphentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012948531&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bollobasbela extremalgraphtheory |