Chromatic polynomials and chromaticity of graphs:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey, NJ [u.a.]
World Scientific
2005
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXVII, 356 S. graph. Darst. |
| ISBN: | 9812563172 |
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| adam_text | CHROMATIC POLYNOMIALS A N D CHROMATICITY OF GRAPHS BY F M DONG NANYANG
TECHNOLOGICAL UNIVERSITY, SINGAPORE KMKOH NATIONAL UNIVERSITY OF
SINGAPORE, SINGAPORE KLTEO MASSEY UNIVERSITY, NEW ZEALAND FC WORLD
SCIENTIFIC NEW JERSEY * LONDON * SINGAPORE * BEI JING * SHANGHAI *
HONGKONG * TAIPEI * CHENNAI CONTENTS PREFACE V BASIC CONCEPTS IN GRAPH
THEORY XV NOTATION XXV 1 THE NUMBER OF A-COLOURINGS AND ITS ENUMERATIONS
1 1.1 INTRODUCTION 1 1.2 EXAMPLES 2 1.3 BASIC RESULTS ON ENUMERATION OF
P(G, A) 4 1.4 P(G, A) IN FACTORIAL FORM 9 1.5 THE JOIN OF GRAPHS AND THE
UMBRAL PRODUCT 12 1.6 P(G,X) IN TREE FORM 14 EXERCISE 1 17 2 CHROMATIC
POLYNOMIALS 23 2.1 INTRODUCTION 23 2.2 AN INTERPRETATION OF THE
COEFFICIENTS 24 2.3 BROKEN-CYCLE THEOREM 26 2.4 THE MULTIPLICITY OF ROOT
1 35 2.5 LEAST COEFFICIENTS 37 2.6 DIVISIBILITY OF THE COEFFICIENTS 42
2.7 UNIMODAL CONJECTURE 47 EXERCISE 2 51 3 CHROMATIC EQUIVALENCE OF
GRAPHS 55 3.1 INTRODUCTION 55 3.2 CHROMATICALLY EQUIVALENT GRAPHS 56 3.3
EQUIVALENCE CLASSES AND - UNIQUE GRAPHS 63 IX X CONTENTS 3.4
DISCONNECTED X-UNIQUE GRAPHS 65 3.5 ONE-CONNECTED X-UNIQUE GRAPHS 66 3.6
X -UMC I UE GRAPHS WITH CONNECTIVITY 2 68 3.7 A CHROMATICALLY
EQUIVALENCE CLASS 71 3.8 FURTHER RESULTS 73 3.8.1 A ^-GLUING OF GRAPHS
73 3.8.2 POLYGON-TREES AND RELATED STRUCTURES 75 3.8.3 2-CONNECTED (N, N
+ &)-GRAPHS WITH SMALL K 76 EXERCISE 3 80 4 CHROMATICITY OF
MULTI-PARTITE GRAPHS 83 4.1 INTRODUCTION 83 4.2 COMPLETE BIPARTITE
GRAPHS 84 4.3 COMPLETE TRIPARTITE GRAPHS 86 4.4 COMPLETE MULTI-PARTITE
GRAPHS 90 4.5 COMPLETE BIPARTITE GRAPHS WITH SOME EDGES DELETED 94 4.6
FURTHER RESULTS 99 EXERCISE 4 101 5 CHROMATICITY OF SUBDIVISIONS OF
GRAPHS 105 5.1 INTRODUCTION 105 5.2 MULTI-BRIDGE GRAPHS 106 5.2.1
CHROMATIC POLYNOMIALS OF MULTI-BRIDGE GRAPHS . . . 106 5.2.2 GENERALIZED
POLYGON-TREES 109 5.2.3 CHROMATICITY OF FC-BRIDGE GRAPHS WITH K = 4,5,6
. . . 111 5.2.4 CHROMATICITY OF GENERAL MULTI-BRIDGE GRAPHS 112 5.3
CHROMATICITY OF GENERALIZED POLYGON-TREES 114 5.4 .FTVHOMEOMORPHS 118
5.5 CHROMATICITY OF UNIFORM SUBDIVISIONS OF GRAPHS 123 5.6 FURTHER
RESULTS 127 EXERCISE 5 130 6 GRAPHS IN WHICH ANY TWO COLOUR CLASSES
INDUCE A TREE (I) 133 6.1 INTRODUCTION 133 6.2 THE SIZES AND TRIANGLE
NUMBERS OF GRAPHS IN T R 135 6.3 GRAPHS IN % 139 6.4 CHORDAL GRAPHS 141
CONTENTS XI 6.5 G-TREES 144 EXERCISE 6 147 7 GRAPHS IN WHICH ANY TWO
COLOUR CLASSES INDUCE A TREE (II) 149 7.1 INTRODUCTION 149 7.2 THE
NUMBER S 3 (H) 151 7.3 THE FAMILY T 3 ,X 153 7.4 THE STRUCTURE OF GRAPHS
IN T R (R 4) 156 7.5 CHROMATICALLY UNIQUE GRAPHS IN T R 161 7.6
FURTHER RESULTS 164 EXERCISE 7 167 8 GRAPHS IN WHICH ALL BUT ONE PAIR OF
COLOUR CLASSES INDUCE TREES (I) 169 8.1 INTRODUCTION 169 8.2 THE
TRIANGLE NUMBER AND AN UPPER BOUND 170 8.3 GRAPHS IN T T HAVING MAXIMUM
TRIANGLE NUMBERS 172 8.4 A MORE GENERAL RESULT 177 EXERCISE 8 178 9
GRAPHS IN WHICH ALL BUT ONE PAIR OF COLOUR CLASSES INDUCE TREES (II) 179
9.1 INTRODUCTION 179 9.2 CLASSIFICATION OF GRAPHS SATISFYING (CT) 180
9.3 GRAPHS IN CT 184 9.4 GRAPHS CONTAINING EXACTLY ONE PURE CYCLE 185
9.5 THE MAIN RESULTS 188 9.6 FURTHER RESULTS 190 EXERCISE 9 193 10
CHROMATICITY OF EXTREMAL 3-COLOURABLE GRAPHS 195 10.1 INTRODUCTION 195
10.2 3-COLOURABLE GRAPHS 197 10.3 A FAMILY OF 3-COLOURABLE GRAPHS 200
10.4 CHROMATICITY OF GRAPHS IN XK 207 EXERCISE 10 213 XII CONTENTS 11
POLYNOMIALS RELATED TO CHROMATIC POLYNOMIALS 215 11.1 INTRODUCTION 215
11.2 BASIC PROPERTIES OF ADJOINT POLYNOMIALS 217 11.3 REDUCTION FORMULAS
FOR ADJOINT POLYNOMIALS 220 11.4 ROOTS OF ADJOINT POLYNOMIALS 222 11.5
INVARIANTS FOR ADJOINTLY EQUIVALENT GRAPHS 226 11.5.1 DEFINITIONS 226
11.5.2 THE ADJ-INVARIANT RI(G) 227 11.5.3 THE ADJ-INVARIANT R 2 (G) 231
11.6 ADJOINTLY EQUIVALENT GRAPHS 233 11.7 FURTHER RESULTS 241 EXERCISE
11 246 12 REAL ROOTS OF CHROMATIC POLYNOMIALS 249 12.1 INTRODUCTION 249
12.2 ROOT-FREE INTERVALS FOR ALL CHROMATIC POLYNOMIALS 250 12.3 REAL
NUMBERS WHICH ARE NOT CHROMATIC ROOTS 256 12.4 UPPER ROOT-FREE INTERVALS
256 12.5 PLANAR GRAPHS 258 12.6 NEAR-TRIANGULATIONS 260 12.7 GRAPHS WITH
HAMILTONIAN PATHS 263 12.8 BIPARTITE GRAPHS 264 12.9 GRAPHS CONTAINING
SPANNING G-TREES 266 12. LOLARGEST NON-INTEGRAL CHROMATIC ROOT 267
12.11UPPER ROOT-FREE INTERVALS WITH RESPECT TO MAXIMUM DEGREES 269
EXERCISE 12 272 13 INTEGRAL ROOTS OF CHROMATIC POLYNOMIALS 273 13.1
INTRODUCTION 273 13.2 CHROMATIC POLYNOMIALS POSSESSED ONLY BY CHORDAL
GRAPHS . . 275 13.3 GRAPHS G * I OF ORDER W{G) +2 277 13.4 DMITRIEV S
PROBLEM 282 EXERCISE 13 286 14 COMPLEX ROOTS OF CHROMATIC POLYNOMIALS
289 14.1 INTRODUCTION 289 14.2 LOCATION OF CHROMATIC ROOTS 290 14.3
CHROMATIC ROOTS WITHIN |Z| 8A 293 CONTENTS XIII 14.4 SUBDIVISIONS 295
14.5 CHROMATIC ROOTS IN THE WHOLE PLANE 297 14.6 REMARKS 298 14.7 POTTS
MODEL 299 EXERCISE 14 307 15 INEQUALITIES ON CHROMATIC POLYNOMIALS 309
15.1 INTRODUCTION 309 15.2 BOUNDS OF CHROMATIC POLYNOMIALS 310 15.3
MAXIMUM CHROMATIC POLYNOMIALS 313 15.4 AN OPEN PROBLEM 318 15.5 MEAN
COLOUR NUMBERS 321 EXERCISE 15 326 BIBLIOGRAPHY 327 INDEX 353
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| any_adam_object | 1 |
| author | Dong, Feng Ming Koh, Khee Meng Teo, Kok-Lay |
| author_facet | Dong, Feng Ming Koh, Khee Meng Teo, Kok-Lay |
| author_role | aut aut aut |
| author_sort | Dong, Feng Ming |
| author_variant | f m d fm fmd k m k km kmk k l t klt |
| building | Verbundindex |
| bvnumber | BV025495277 |
| classification_rvk | SK 890 |
| ctrlnum | (OCoLC)917806232 (DE-599)BVBBV025495277 |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:35:20Z |
| institution | BVB |
| isbn | 9812563172 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020107469 |
| oclc_num | 917806232 |
| open_access_boolean | |
| owner | DE-11 |
| owner_facet | DE-11 |
| physical | XXVII, 356 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Dong, Feng Ming Verfasser aut Chromatic polynomials and chromaticity of graphs F. M. Dong ; K. M. Koh ; K. L. Teo New Jersey, NJ [u.a.] World Scientific 2005 XXVII, 356 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chromatisches Polynom (DE-588)4338062-1 gnd rswk-swf Graph (DE-588)4021842-9 gnd rswk-swf Chromatisches Polynom (DE-588)4338062-1 s Graph (DE-588)4021842-9 s DE-604 Koh, Khee Meng Verfasser aut Teo, Kok-Lay Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020107469&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dong, Feng Ming Koh, Khee Meng Teo, Kok-Lay Chromatic polynomials and chromaticity of graphs Chromatisches Polynom (DE-588)4338062-1 gnd Graph (DE-588)4021842-9 gnd |
| subject_GND | (DE-588)4338062-1 (DE-588)4021842-9 |
| title | Chromatic polynomials and chromaticity of graphs |
| title_auth | Chromatic polynomials and chromaticity of graphs |
| title_exact_search | Chromatic polynomials and chromaticity of graphs |
| title_full | Chromatic polynomials and chromaticity of graphs F. M. Dong ; K. M. Koh ; K. L. Teo |
| title_fullStr | Chromatic polynomials and chromaticity of graphs F. M. Dong ; K. M. Koh ; K. L. Teo |
| title_full_unstemmed | Chromatic polynomials and chromaticity of graphs F. M. Dong ; K. M. Koh ; K. L. Teo |
| title_short | Chromatic polynomials and chromaticity of graphs |
| title_sort | chromatic polynomials and chromaticity of graphs |
| topic | Chromatisches Polynom (DE-588)4338062-1 gnd Graph (DE-588)4021842-9 gnd |
| topic_facet | Chromatisches Polynom Graph |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020107469&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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