Algorithmic graph theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge u.a.
Cambridge Univ. Press
1999
|
| Edition: | transferred to digital pr. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 259 S. |
| ISBN: | 0521288819 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804130307290431488 |
|---|---|
| adam_text | Contents
Preface
(xi)
1
Introducing graphs and algorithmic complexity
1
1.1
Introducing graphs
1
1.2
Introducing algorithmic complexity
8
1.3
Introducing data structures and depth-first searching
16
1.3.1.
Adjacency matrices and adjacency lists
17
1.3.2.
Depth-first searching
20
1.3.3.
Two linear-time algorithms
24
1.4
Summary and references
32
Exercises
33
2
Spanning-trees, branchings and connectivity
39
2.1
Spanning-trees and branchings
39
2.1.1.
Optimum weight spanning-trees
40
2.1.2.
Optimum branchings
42
2.1.3.
Enumeration of spanning-trees
49
2.2
Circuits, cut-sets and connectivity
54
2.2.1.
Fundamental circuits of a graph
54
2.2.2.
Fundamental cut-sets of a graph
57
2.2.3.
Connectivity
60
2.3
Summary and references
62
Exercises
63
3
Planar graphs
67
3.1
Basic properties of planar graphs
67
3.2
Genus, crossing-number and thickness
71
3.3
Characterisations of planarity
75
3.3.1.
Dual graphs
81
3.4
A planarity testing algorithm
85
3.5
Summary and references
92
Exercises
93
viii Contents
4
Networks
and flows
96
4.1
Networks and flows
96
4.2
Maximising the flow in a network
98
4.3
Menger s theorems and connectivity
106
4.4
A minimum-cost flow algorithm 111
4.5
Summary and references
118
Exercises
120
5
Matchings
125
5.1
Definitions
125
5.2
Maximum-cardinality matchings
126
5.2.1.
Perfect matchings
134
5.3
Maximum-weight matchings
136
5.4
Summary and references
147
Exercises
148
6
Eulerian and Hamiltonian tours
153
6.1
Eulerian paths and circuits
153
6.1.1.
Eulerian graphs
155
6.1.2.
Finding Eulerian circuits
156
6.2
Postman problems
161
6.2.1.
Counting Eulerian circuits
162
6.2.2.
The Chinese postman problem for undirected graphs
163
6.2.3.
The Chinese postman problem for digraphs
165
6.3
Hamiltonian tours
169
6.3.1.
Some elementary existence theorems
169
6.3.2.
Finding all Hamiltonian tours by
matricial
products
173
6.3.3.
The travelling salesman problem
175
6.3.4.
2-factors of a graph
182
6.4
Summary and references
184
Exercises
185
7
Colouring graph»
189
7.1
Dominating sets, independence and cliques
189
7.2
Colouring graphs
195
7.2.1.
Edge-colouring
195
7.2.2.
Vertex-colouring
198
7.2.3.
Chromatic polynomials
201
7.3
Face-colourings of embedded graphs
204
7.3.1.
The five-colour theorem
204
7.3.2.
The four-colour theorem
207
7.4
Summary and references
210
Exercises
212
8
Graph problems and intractability
217
8.1
Introduction to iVP-completeness
217
Contents ix
8.1.1.
The classes
Ρ
and
NP
217
8.1.2.
W-completeness and Cook s theorem
222
8.2
W-complete
graph problems
227
8.2.1.
Problems of vertex cover, independent set and clique
227
8.2.2.
Problems of Hamiltonian paths and circuits and the
travelling salesman problem
229
8.2.3.
Problems concerning the colouring of graphs
235
8.3
Concluding comments
241
8.4
Summary and references
244
Exercises
245
Appendix: On linear programming
249
Author index
254
Subject index
256
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | transferred to digital pr. |
| format | Book |
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| id | DE-604.BV017518533 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:18:57Z |
| institution | BVB |
| isbn | 0521288819 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010550895 |
| oclc_num | 551949161 |
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| owner_facet | DE-91G DE-BY-TUM DE-355 DE-BY-UBR |
| physical | XII, 259 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Gibbons, Alan Verfasser aut Algorithmic graph theory Alan Gibbons transferred to digital pr. Cambridge u.a. Cambridge Univ. Press 1999 XII, 259 S. txt rdacontent n rdamedia nc rdacarrier Graphentheorie (DE-588)4113782-6 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s Algorithmus (DE-588)4001183-5 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010550895&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gibbons, Alan Algorithmic graph theory Graphentheorie (DE-588)4113782-6 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4001183-5 |
| title | Algorithmic graph theory |
| title_auth | Algorithmic graph theory |
| title_exact_search | Algorithmic graph theory |
| title_full | Algorithmic graph theory Alan Gibbons |
| title_fullStr | Algorithmic graph theory Alan Gibbons |
| title_full_unstemmed | Algorithmic graph theory Alan Gibbons |
| title_short | Algorithmic graph theory |
| title_sort | algorithmic graph theory |
| topic | Graphentheorie (DE-588)4113782-6 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Graphentheorie Algorithmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010550895&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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