Modern graph theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
[2010]
|
| Ausgabe: | 5. print. |
| Schriftenreihe: | Graduate texts in mathematics
184 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XIII, 394 S. graph. Darst. |
| ISBN: | 0387984887 0387984917 9780387984889 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV037441880 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 110607s2010 d||| |||| 00||| eng d | ||
| 020 | |a 0387984887 |c pbk. |9 0-387-98488-7 | ||
| 020 | |a 0387984917 |c hbk. |9 0-387-98491-7 | ||
| 020 | |a 9780387984889 |c pbk. |9 978-0-387-98488-9 | ||
| 035 | |a (OCoLC)845712663 | ||
| 035 | |a (DE-599)GBV620008199 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-11 | ||
| 082 | 0 | |a 511.5 | |
| 084 | |a SK 890 |0 (DE-625)143267: |2 rvk | ||
| 084 | |a ST 130 |0 (DE-625)143588: |2 rvk | ||
| 100 | 1 | |a Bollobás, Béla |d 1943- |e Verfasser |0 (DE-588)109481240 |4 aut | |
| 245 | 1 | 0 | |a Modern graph theory |c Béla Bollobás |
| 250 | |a 5. print. | ||
| 264 | 1 | |a New York, NY |b Springer |c [2010] | |
| 300 | |a XIII, 394 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 184 | |
| 500 | |a Literaturangaben | ||
| 650 | 0 | 7 | |a Graphentheorie |0 (DE-588)4113782-6 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Graphentheorie |0 (DE-588)4113782-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Graduate texts in mathematics |v 184 |w (DE-604)BV000000067 |9 184 | |
| 856 | 4 | |m DE-601 |q pdf/application |u http://www.zentralblatt-math.org/zmath/en/search/?an=0902.05016 |y Zentralblatt MATH |z kostenfrei |3 Inhaltstext | |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022593792&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-022593792 | ||
Datensatz im Suchindex
| _version_ | 1804145753579323392 |
|---|---|
| adam_text | IMAGE 1
B61A BOLLOBAS
MODERN GRAPH THEORY
WITH 118 FIGURES
|Y SPRINGER
IMAGE 2
CONTENTS
APOLOGIA VII
PREFACE IX
I FUNDAMENTALS 1
1.1 DEFINITIONS 1
1.2 PATHS, CYCLES, AND TREES 8
1.3 HAMILTON CYCLES AND EULER CIRCUITS 14
1.4 PLANAR GRAPHS 20
1.5 AN APPLICATION OF EULER TRAILS TO ALGEBRA 25
1.6 EXERCISES 28
II ELECTRICAL NETWORKS 39
II. 1 GRAPHS AND ELECTRICAL NETWORKS 39
11.2 SQUARING THE SQUARE * 46
11.3 VECTOR SPACES AND MATRICES ASSOCIATED WITH GRAPHS . . .. 51 11.4
EXERCISES . 58
11.5 NOTES 66
III FLOWS, CONNECTIVITY AND MATCHING 67
III. 1 FLOWS IN DIRECTED GRAPHS 68
111.2 CONNECTIVITY AND MENGER S THEOREM 73
111.3 MATCHING 76
111.4 TUTTE S 1-FACTOR THEOREM 82
IMAGE 3
XII CONTENTS
111.5 STABLE MATCHINGS 85
111.6 EXERCISES 91
111.7 NOTES 101
IV EXTREMAL PROBLEMS 103
IV.L PATHS AND CYCLES 104
IV.2 COMPLETE SUBGRAPHS 108
IV.3 HAMILTON PATHS AND CYCLES 115
IV.4 THE STRUCTURE OF GRAPHS 120
FV.5 SZEMEREDI S REGULARITY LEMMA 124
IV.6 SIMPLE APPLICATIONS OF SZEMEREDI S LEMMA 130
IV.7 EXERCISES 135
IV.8 NOTES 142
V COLOURING 145
V.I VERTEX COLOURING 146
V.2 EDGE COLOURING 152
V.3 GRAPHS ON SURFACES 154
V.4 LIST COLOURING 161
V.5 PERFECT GRAPHS 165
V.6 EXERCISES 170
V.7 NOTES 177
VI RAMSEY THEORY 181
VI. 1 THE FUNDAMENTAL RAMSEY THEOREMS 182
VI.2 CANONICAL RAMSEY THEOREMS 189
VI.3 RAMSEY THEORY FOR GRAPHS 192
VI.4 RAMSEY THEORY FOR INTEGERS 197
VI.5 SUBSEQUENCES 205
VI.6 EXERCISES 208
VI.7 NOTES 213
VII RANDOM GRAPHS 215
VII. 1 THE BASIC MODELS-THE USE OF THE EXPECTATION 216 VII.2 SIMPLE
PROPERTIES OF ALMOST ALL GRAPHS 225
VII.3 ALMOST DETERMINED VARIABLES-THE USE OF THE VARIANCE . . 228 VII.4
HAMILTON CYCLES-THE USE OF GRAPH THEORETIC TOOLS . . .. 236 VII.5 THE
PHASE TRANSITION 240
VII.6 EXERCISES 246
VII.7 NOTES 251
VIII GRAPHS, GROUPS AND MATRICES 253
VIII. 1 CAY LEY AND SCHREIER DIAGRAMS 254
VIII.2 THE ADJACENCY MATRIX AND THE LAPLACIAN 262
VIII.3 STRONGLY REGULAR GRAPHS 270
IMAGE 4
CONTENTS XIII
VIII.4 ENUMERATION AND POLYA S THEOREM 276
VIII.5 EXERCISES 283
IX RANDOM WALKS ON GRAPHS 295
IX. 1 ELECTRICAL NETWORKS REVISITED 296
IX.2 ELECTRICAL NETWORKS AND RANDOM WALKS 301
IX.3 HITTING TIMES AND COMMUTE TIMES 309
IX.4 CONDUCTANCE AND RAPID MIXING 319
IX.5 EXERCISES 327
IX.6 NOTES 333
X THE TUTTE POLYNOMIAL 335
X. 1 BASIC PROPERTIES OF THE TUTTE POLYNOMIAL 336
X.2 THE UNIVERSAL FORM OF THE TUTTE POLYNOMIAL 340
X.3 THE TUTTE POLYNOMIAL IN STATISTICAL MECHANICS 342
X.4 SPECIAL VALUES OF THE TUTTE POLYNOMIAL 345
X.5 A SPANNING TREE EXPANSION OF THE TUTTE POLYNOMIAL . . .. 350 X.6
POLYNOMIALS OF KNOTS AND LINKS 358
X.7 EXERCISES 371
X.8 NOTES 377
SYMBOL INDEX 379
NAME INDEX 383
SUBJECT INDEX 387
|
| any_adam_object | 1 |
| author | Bollobás, Béla 1943- |
| author_GND | (DE-588)109481240 |
| author_facet | Bollobás, Béla 1943- |
| author_role | aut |
| author_sort | Bollobás, Béla 1943- |
| author_variant | b b bb |
| building | Verbundindex |
| bvnumber | BV037441880 |
| classification_rvk | SK 890 ST 130 |
| ctrlnum | (OCoLC)845712663 (DE-599)GBV620008199 |
| 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 | 3511.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 5. print. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01710nam a2200433 cb4500</leader><controlfield tag="001">BV037441880</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">110607s2010 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387984887</subfield><subfield code="c">pbk.</subfield><subfield code="9">0-387-98488-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387984917</subfield><subfield code="c">hbk.</subfield><subfield code="9">0-387-98491-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780387984889</subfield><subfield code="c">pbk.</subfield><subfield code="9">978-0-387-98488-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)845712663</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)GBV620008199</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-11</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.5</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 890</subfield><subfield code="0">(DE-625)143267:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">ST 130</subfield><subfield code="0">(DE-625)143588:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bollobás, Béla</subfield><subfield code="d">1943-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)109481240</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Modern graph theory</subfield><subfield code="c">Béla Bollobás</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">5. print.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY</subfield><subfield code="b">Springer</subfield><subfield code="c">[2010]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 394 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">184</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturangaben</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Graphentheorie</subfield><subfield code="0">(DE-588)4113782-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4123623-3</subfield><subfield code="a">Lehrbuch</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Graphentheorie</subfield><subfield code="0">(DE-588)4113782-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">184</subfield><subfield code="w">(DE-604)BV000000067</subfield><subfield code="9">184</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="m">DE-601</subfield><subfield code="q">pdf/application</subfield><subfield code="u">http://www.zentralblatt-math.org/zmath/en/search/?an=0902.05016</subfield><subfield code="y">Zentralblatt MATH</subfield><subfield code="z">kostenfrei</subfield><subfield code="3">Inhaltstext</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">GBV Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022593792&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-022593792</subfield></datafield></record></collection> |
| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV037441880 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:24:28Z |
| institution | BVB |
| isbn | 0387984887 0387984917 9780387984889 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022593792 |
| oclc_num | 845712663 |
| open_access_boolean | 1 |
| owner | DE-11 |
| owner_facet | DE-11 |
| physical | XIII, 394 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Bollobás, Béla 1943- Verfasser (DE-588)109481240 aut Modern graph theory Béla Bollobás 5. print. New York, NY Springer [2010] XIII, 394 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 184 Literaturangaben Graphentheorie (DE-588)4113782-6 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Graphentheorie (DE-588)4113782-6 s DE-604 Graduate texts in mathematics 184 (DE-604)BV000000067 184 DE-601 pdf/application http://www.zentralblatt-math.org/zmath/en/search/?an=0902.05016 Zentralblatt MATH kostenfrei Inhaltstext GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022593792&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bollobás, Béla 1943- Modern graph theory Graduate texts in mathematics Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4123623-3 |
| title | Modern graph theory |
| title_auth | Modern graph theory |
| title_exact_search | Modern graph theory |
| title_full | Modern graph theory Béla Bollobás |
| title_fullStr | Modern graph theory Béla Bollobás |
| title_full_unstemmed | Modern graph theory Béla Bollobás |
| title_short | Modern graph theory |
| title_sort | modern graph theory |
| topic | Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Graphentheorie Lehrbuch |
| url | http://www.zentralblatt-math.org/zmath/en/search/?an=0902.05016 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022593792&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT bollobasbela moderngraphtheory |