Chromatic graph theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2009
|
| Series: | Discrete mathematics and its applications
53 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIV, 483 S. graph. Darst. |
| ISBN: | 9781584888000 1584888008 |
Staff View
MARC
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| 100 | 1 | |a Chartrand, Gary |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Chromatic graph theory |c Gary Chartrand, Ping Zhang |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2009 | |
| 300 | |a XIV, 483 S. |b graph. Darst. | ||
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| 490 | 1 | |a Discrete mathematics and its applications |v 53 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 7 | |a Grafentheorie |2 gtt | |
| 650 | 4 | |a Graph coloring | |
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Record in the Search Index
| _version_ | 1804138354440142848 |
|---|---|
| adam_text | Table
of
Contents
0.
The Origin of Graph Colorings
1
1.
Introduction to Graphs
27
1.1
Fundamental Terminology
27
1.2
Connected Graphs
30
1.3
Distance in Graphs
33
1.4
Isomorphic Graphs
37
1.5
Common Graphs and Graph Operations
39
1.6
Multigraphs and Digraphs
44
Exercises for Chapter
1 47
2.
Trees and Connectivity
53
2.1
Cut-vertices, Bridges, and Blocks
53
2.2
Trees
56
2.3
Connectivity and Edge-Connectivity
59
2.4
Menger s Theorem
63
Exercises for Chapter
2 67
3.
Eulerian and Hamiltonian Graphs
71
3.1
Eulerian Graphs
71
3.2
de Bruijn
Digraphs
76
3.3
Hamiltonian Graphs
79
Exercises for Chapter
3 87
4.
Matchings and Factorization
91
4.1
Matchings
91
4.2
Independence in Graphs
98
4.3
Factors and Factorization
100
Exercises for Chapter
4 106
5.
Graph Embeddings
109
5.1
Planar Graphs and the
Euler
Identity
109
5.2
Hamiltonian Planar Graphs
118
ix
5.3
Planarity Versus Nonplanarity
120
5.4
Embedding Graphs on Surfaces
131
5.5
The Graph Minor Theorem
139
Exercises for Chapter
5 141
6.
Introduction to Vertex Colorings
147
6.1
The Chromatic Number of a Graph
147
6.2
Applications of Colorings
153
6.3
Perfect Graphs
160
Exercises for Chapter
6 170
7.
Bounds for the Chromatic Number
175
7.1
Color-Critical Graphs
175
7.2
Upper Bounds and Greedy Colorings
179
7.3
Upper Bounds and Oriented Graphs
189
7.4
The Chromatic Number of Cartesian Products
195
Exercises for Chapter
7 200
8.
Coloring Graphs on Surfaces
205
8.1
The Four Color Problem
205
8.2
The Conjectures of
Hajós
and Hadwiger
208
8.3
Chromatic Polynomials
211
8.4
The Heawood Map-Coloring Problem
217
Exercises for Chapter
8 219
9.
Restricted Vertex Colorings
223
9.1
Uniquely Colorable Graphs
223
9.2
List Colorings
230
9.3
Precoloring Extensions of Graphs
240
Exercises for Chapter
9 245
10.
Edge Colorings of Graphs
249
10.1
The Chromatic Index and Vizing s Theorem
249
10.2
Class One and Class Two Graphs
255
10.3
Tait
Colorings
262
10.4
Nowhere-Zero Flows
269
10.5
List Edge Colorings
279
10.6 Total
Colorings of Graphs
282
Exercises for Chapter
10 284
11.
Monochromatic and Rainbow Colorings
289
11.1
Ramsey Numbers
289
11.2
Turán s
Theorem
296
11.3
Rainbow Ramsey Numbers
299
11.4
Rainbow Numbers of Graphs
306
11.5
Rainbow-Connected Graphs
314
11.6
The Road Coloring Problem
320
Exercises for Chapter
11 324
12.
Complete Colorings
329
12.1
The Achromatic Number of a Graph
329
12.2
Graph Homomorphisms
335
12.3
The Grundy Number of a Graph
349
Exercises for Chapter
12 356
13.
Distinguishing Colorings
359
13.1
Edge-Distinguishing Vertex Colorings
359
13.2
Vertex-Distinguishing Edge Colorings
370
13.3
Vertex-Distinguishing Vertex Colorings
379
13.4
Neighbor-Distinguishing Edge Colorings
385
Exercises for Chapter
13 391
14.
Colorings, Distance, and Domination
397
14.1
T-Colorings
397
14.2
L(2,l)-Colorings
403
14.3
Radio Colorings
410
14.4
Hamiltonian Colorings
417
14.5
Domination and Colorings
425
14.6
Epilogue
434
Exercises for Chapter
14 434
Appendix: Study Projects
439
General References
446
Bibliography
453
Index (Names and Mathematical Terms)
465
List of Symbols
480
xi
|
| adam_txt |
Table
of
Contents
0.
The Origin of Graph Colorings
1
1.
Introduction to Graphs
27
1.1
Fundamental Terminology
27
1.2
Connected Graphs
30
1.3
Distance in Graphs
33
1.4
Isomorphic Graphs
37
1.5
Common Graphs and Graph Operations
39
1.6
Multigraphs and Digraphs
44
Exercises for Chapter
1 47
2.
Trees and Connectivity
53
2.1
Cut-vertices, Bridges, and Blocks
53
2.2
Trees
56
2.3
Connectivity and Edge-Connectivity
59
2.4
Menger's Theorem
63
Exercises for Chapter
2 67
3.
Eulerian and Hamiltonian Graphs
71
3.1
Eulerian Graphs
71
3.2
de Bruijn
Digraphs
76
3.3
Hamiltonian Graphs
79
Exercises for Chapter
3 87
4.
Matchings and Factorization
91
4.1
Matchings
91
4.2
Independence in Graphs
98
4.3
Factors and Factorization
100
Exercises for Chapter
4 106
5.
Graph Embeddings
109
5.1
Planar Graphs and the
Euler
Identity
109
5.2
Hamiltonian Planar Graphs
118
ix
5.3
Planarity Versus Nonplanarity
120
5.4
Embedding Graphs on Surfaces
131
5.5
The Graph Minor Theorem
139
Exercises for Chapter
5 141
6.
Introduction to Vertex Colorings
147
6.1
The Chromatic Number of a Graph
147
6.2
Applications of Colorings
153
6.3
Perfect Graphs
160
Exercises for Chapter
6 170
7.
Bounds for the Chromatic Number
175
7.1
Color-Critical Graphs
175
7.2
Upper Bounds and Greedy Colorings
179
7.3
Upper Bounds and Oriented Graphs
189
7.4
The Chromatic Number of Cartesian Products
195
Exercises for Chapter
7 200
8.
Coloring Graphs on Surfaces
205
8.1
The Four Color Problem
205
8.2
The Conjectures of
Hajós
and Hadwiger
208
8.3
Chromatic Polynomials
211
8.4
The Heawood Map-Coloring Problem
217
Exercises for Chapter
8 219
9.
Restricted Vertex Colorings
223
9.1
Uniquely Colorable Graphs
223
9.2
List Colorings
230
9.3
Precoloring Extensions of Graphs
240
Exercises for Chapter
9 245
10.
Edge Colorings of Graphs
249
10.1
The Chromatic Index and Vizing's Theorem
249
10.2
Class One and Class Two Graphs
255
10.3
Tait
Colorings
262
10.4
Nowhere-Zero Flows
269
10.5
List Edge Colorings
279
10.6 Total
Colorings of Graphs
282
Exercises for Chapter
10 284
11.
Monochromatic and Rainbow Colorings
289
11.1
Ramsey Numbers
289
11.2
Turán's
Theorem
296
11.3
Rainbow Ramsey Numbers
299
11.4
Rainbow Numbers of Graphs
306
11.5
Rainbow-Connected Graphs
314
11.6
The Road Coloring Problem
320
Exercises for Chapter
11 324
12.
Complete Colorings
329
12.1
The Achromatic Number of a Graph
329
12.2
Graph Homomorphisms
335
12.3
The Grundy Number of a Graph
349
Exercises for Chapter
12 356
13.
Distinguishing Colorings
359
13.1
Edge-Distinguishing Vertex Colorings
359
13.2
Vertex-Distinguishing Edge Colorings
370
13.3
Vertex-Distinguishing Vertex Colorings
379
13.4
Neighbor-Distinguishing Edge Colorings
385
Exercises for Chapter
13 391
14.
Colorings, Distance, and Domination
397
14.1
T-Colorings
397
14.2
L(2,l)-Colorings
403
14.3
Radio Colorings
410
14.4
Hamiltonian Colorings
417
14.5
Domination and Colorings
425
14.6
Epilogue
434
Exercises for Chapter
14 434
Appendix: Study Projects
439
General References
446
Bibliography
453
Index (Names and Mathematical Terms)
465
List of Symbols
480
xi |
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| illustrated | Illustrated |
| index_date | 2024-07-02T22:57:58Z |
| indexdate | 2024-07-09T21:26:51Z |
| institution | BVB |
| isbn | 9781584888000 1584888008 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016987957 |
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| physical | XIV, 483 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
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| publisher | CRC Press |
| record_format | marc |
| series | Discrete mathematics and its applications |
| series2 | Discrete mathematics and its applications |
| spelling | Chartrand, Gary Verfasser aut Chromatic graph theory Gary Chartrand, Ping Zhang Boca Raton [u.a.] CRC Press 2009 XIV, 483 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Discrete mathematics and its applications 53 Includes bibliographical references and index Grafentheorie gtt Graph coloring Graphfärbung (DE-588)4472286-2 gnd rswk-swf Graphfärbung (DE-588)4472286-2 s DE-604 Zhang, Ping Verfasser aut Discrete mathematics and its applications 53 (DE-604)BV023551867 53 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016987957&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chartrand, Gary Zhang, Ping Chromatic graph theory Discrete mathematics and its applications Grafentheorie gtt Graph coloring Graphfärbung (DE-588)4472286-2 gnd |
| subject_GND | (DE-588)4472286-2 |
| title | Chromatic graph theory |
| title_auth | Chromatic graph theory |
| title_exact_search | Chromatic graph theory |
| title_exact_search_txtP | Chromatic graph theory |
| title_full | Chromatic graph theory Gary Chartrand, Ping Zhang |
| title_fullStr | Chromatic graph theory Gary Chartrand, Ping Zhang |
| title_full_unstemmed | Chromatic graph theory Gary Chartrand, Ping Zhang |
| title_short | Chromatic graph theory |
| title_sort | chromatic graph theory |
| topic | Grafentheorie gtt Graph coloring Graphfärbung (DE-588)4472286-2 gnd |
| topic_facet | Grafentheorie Graph coloring Graphfärbung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016987957&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT chartrandgary chromaticgraphtheory AT zhangping chromaticgraphtheory |