Topics in topological graph theory:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Encyclopedia of mathematics and its applications
128 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 347 S. Ill., graph. Darst. |
| ISBN: | 9780521802307 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV035768771 | ||
| 003 | DE-604 | ||
| 005 | 20111108 | ||
| 007 | t | ||
| 008 | 091014s2009 ad|| |||| 00||| eng d | ||
| 020 | |a 9780521802307 |9 978-0-521-80230-7 | ||
| 035 | |a (OCoLC)311769303 | ||
| 035 | |a (DE-599)HBZHT016001551 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-703 |a DE-19 |a DE-824 | ||
| 050 | 0 | |a QA166.195 | |
| 082 | 0 | |a 511.5 |2 22 | |
| 084 | |a SK 890 |0 (DE-625)143267: |2 rvk | ||
| 245 | 1 | 0 | |a Topics in topological graph theory |c ed. by Lowell W. Beineke ... |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2009 | |
| 300 | |a XVIII, 347 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Encyclopedia of mathematics and its applications |v 128 | |
| 650 | 4 | |a Topological graph theory | |
| 650 | 0 | 7 | |a Topologische Graphentheorie |0 (DE-588)4341226-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Topologische Graphentheorie |0 (DE-588)4341226-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Beineke, Lowell W. |e Sonstige |0 (DE-588)142229997 |4 oth | |
| 830 | 0 | |a Encyclopedia of mathematics and its applications |v 128 |w (DE-604)BV000903719 |9 128 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018628511&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018628511 | ||
Datensatz im Suchindex
| _version_ | 1804140697256722432 |
|---|---|
| adam_text | Contents
Foreword by Jonathan
L.
Gross and Thomas W. Tucker page
xv
Preface
xvii
Introduction
1
LOWELL W. BEINEKE and ROBIN J. WILSON
1.
Graph theory
1
2.
Graphs in the plane
10
3.
Surfaces
12
4.
Graphs on surfaces
14
1
Embedding graphs on surfaces
18
JONATHAN L. GROSS and THOMAS W. TUCKER
1.
Introduction
18
2.
Graphs and surfaces
19
3.
Embeddings
20
4.
Rotation systems
23
5.
Covering spaces and voltage graphs
26
6.
Enumeration
29
7.
Algorithms
30
8.
Graph minors
31
2
Maximum genus
34
IIANER CHEN and YUANQIU HUANG
1.
Introduction
34
2.
Characterizations and complexity
36
3.
Kuratowski-rype theorems
38
4.
Upper-embeddability
39
5.
Lower bounds
40
ix
x
Contents
3 Distribution
of embeddings
45
JONATHAN L. GROSS
1.
Introduction
45
2.
Enumerating embeddings by surface type
48
3.
Total embedding distributions
51
4.
Congruence classes
53
5.
The unimodality problem
55
6.
Average genus
56
7.
Stratification of embeddings
59
4
Algorithms and obstructions for embeddings
62
BOJAN MOHÄR
1.
Introduction
62
2.
Planarity
64
3.
Outerplanarity and face covers
66
4.
Disc embeddings and the 2-path problem
68
5.
Graph minors and obstructions
69
6.
Algorithms for embeddability in general surfaces
73
7.
Computing the genus
75
5
Graph minors: generalizing Kuratowski s theorem
81
R. BRUCE
RICHTER
1.
Introduction
81
2.
Graph decompositions
84
3.
Linked decompositions
88
4.
Graphs with bounded tree-width
94
5.
Finding large grids
99
6.
Embedding large grids
107
6
Colouring graphs on surfaces 111
JOAN P. HUTCHINSON
1.
Introduction 111
2.
High-end colouring
113
3.
A transition from high-end to low-end colouring
116
4.
Colouring graphs with few colours
119
5.
Girth and chromatic number
124
6.
List-colouring graphs
125
7.
More colouring extensions
127
8.
An open problem
129
Contents xi
7 Crossing
numbers
133
R.
BRUCE RICHTER
and G SALAZAR
1.
Introduction
133
2.
What is the crossing number?
135
3.
General bounds
137
4.
Applications to geometry
139
5.
Crossing-critical graphs
139
6.
Other families of graphs
143
7.
Algorithmic questions
144
8.
Drawings in other surfaces
146
9.
Conclusion
147
8
Representing graphs and maps
151
TOMAŽ
PISANSKI and ARJANA
ŽITNIK
1.
Introduction
151
2.
Representations of graphs
152
3.
Energy and optimal representations
155
4.
Representations of maps
163
5.
Representations of maps in the plane
170
6.
Representations of incidence geometries and related topics
174
9
Enumerating coverings
181
JIN HO
KWAK
and JAEUN LEE
1.
Introduction
181
2.
Graph coverings
183
3.
Regular coverings
185
4.
Surface branched coverings
190
5.
Regular surface branched coverings
193
6.
Distribution of surface branched coverings
195
7. Furtherremarks 196
10
Symmetric maps
199
JOZEF ŠIRÁŇ
and THOMAS W. TUCKER
1.
Introduction
199
2.
Representing maps algebraically
200
3.
Regular maps
205
4.
Cayley maps
210
5.
Regular Cayley maps
212
6.
Edge-transitive maps
218
7.
Maps and mathematics
221
xii Contents
11
The genus of a group
225
THOMAS W. TUCKER
1.
Introduction
225
2.
Symmetric embeddings and groups acting on surfaces
226
3.
Quotient embeddings and voltage graphs
228
4.
Inequalities
232
5.
Groups of low genus
235
6.
Genera of families of groups
239
12
Embeddings and geometries
245
ARTHUR T. WHITE
1.
Introduction
245
2.
Surface models
248
3.
Projective
geometries
250
4. Affine
geometries
253
5.
3-configurations
256
6.
Partial geometries
260
7.
Regular embeddings for PG(2, n)
264
8.
Problems
265
13
Embeddings and designs
268
M. J. GRANNELL and T. S. GRIGGS
1.
Introduction
268
2. Steiner
triple systems and
triangulations
270
3.
Recursive constructions
273
4.
Small systems
278
5.
Cyclic embeddings
280
6.
Concluding remarks
284
14
Infinite graphs and planar maps
289
MARK E. WATKINS
1.
Introduction
289
2.
Ends
290
3.
Automorphisms
293
4.
Connectivities
295
5.
Growth
300
6.
Infinite planar graphs and maps
303
Contents xiii
15
Open problems
313
DAN ARCHDEACON
1.
Introduction
313
2.
Drawings and crossings
314
3.
Genus and obstructions
317
4.
Cycles and factors
320
5.
Colourings and flows
322
6.
Local planarity
324
7.
Thickness, book embeddings and covering graphs
325
8.
Geometrical topics
328
9.
Algorithms
330
10.
Infinite graphs
332
Notes on contributors
337
Index
341
|
| any_adam_object | 1 |
| author_GND | (DE-588)142229997 |
| building | Verbundindex |
| bvnumber | BV035768771 |
| callnumber-first | Q - Science |
| callnumber-label | QA166 |
| callnumber-raw | QA166.195 |
| callnumber-search | QA166.195 |
| callnumber-sort | QA 3166.195 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 890 |
| ctrlnum | (OCoLC)311769303 (DE-599)HBZHT016001551 |
| 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 | Mathematik |
| edition | 1. publ. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01536nam a2200385 cb4500</leader><controlfield tag="001">BV035768771</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20111108 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">091014s2009 ad|| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780521802307</subfield><subfield code="9">978-0-521-80230-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)311769303</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)HBZHT016001551</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-824</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA166.195</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.5</subfield><subfield code="2">22</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="245" ind1="1" ind2="0"><subfield code="a">Topics in topological graph theory</subfield><subfield code="c">ed. by Lowell W. Beineke ...</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. publ.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge [u.a.]</subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">2009</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVIII, 347 S.</subfield><subfield code="b">Ill., 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">Encyclopedia of mathematics and its applications</subfield><subfield code="v">128</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Topological graph theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Topologische Graphentheorie</subfield><subfield code="0">(DE-588)4341226-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Topologische Graphentheorie</subfield><subfield code="0">(DE-588)4341226-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Beineke, Lowell W.</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)142229997</subfield><subfield code="4">oth</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Encyclopedia of mathematics and its applications</subfield><subfield code="v">128</subfield><subfield code="w">(DE-604)BV000903719</subfield><subfield code="9">128</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth</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=018628511&sequence=000002&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:BVB01-018628511</subfield></datafield></record></collection> |
| id | DE-604.BV035768771 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:06Z |
| institution | BVB |
| isbn | 9780521802307 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018628511 |
| oclc_num | 311769303 |
| open_access_boolean | |
| owner | DE-703 DE-19 DE-BY-UBM DE-824 |
| owner_facet | DE-703 DE-19 DE-BY-UBM DE-824 |
| physical | XVIII, 347 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Topics in topological graph theory ed. by Lowell W. Beineke ... 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2009 XVIII, 347 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 128 Topological graph theory Topologische Graphentheorie (DE-588)4341226-9 gnd rswk-swf Topologische Graphentheorie (DE-588)4341226-9 s DE-604 Beineke, Lowell W. Sonstige (DE-588)142229997 oth Encyclopedia of mathematics and its applications 128 (DE-604)BV000903719 128 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018628511&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Topics in topological graph theory Encyclopedia of mathematics and its applications Topological graph theory Topologische Graphentheorie (DE-588)4341226-9 gnd |
| subject_GND | (DE-588)4341226-9 |
| title | Topics in topological graph theory |
| title_auth | Topics in topological graph theory |
| title_exact_search | Topics in topological graph theory |
| title_full | Topics in topological graph theory ed. by Lowell W. Beineke ... |
| title_fullStr | Topics in topological graph theory ed. by Lowell W. Beineke ... |
| title_full_unstemmed | Topics in topological graph theory ed. by Lowell W. Beineke ... |
| title_short | Topics in topological graph theory |
| title_sort | topics in topological graph theory |
| topic | Topological graph theory Topologische Graphentheorie (DE-588)4341226-9 gnd |
| topic_facet | Topological graph theory Topologische Graphentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018628511&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000903719 |
| work_keys_str_mv | AT beinekelowellw topicsintopologicalgraphtheory |