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Brooks' Theorem [[electronic resource] ] : Graph Coloring and Critical Graphs / / by Michael Stiebitz, Thomas Schweser, Bjarne Toft
| Brooks' Theorem [[electronic resource] ] : Graph Coloring and Critical Graphs / / by Michael Stiebitz, Thomas Schweser, Bjarne Toft |
| Autore | Stiebitz Michael |
| Edizione | [1st ed. 2024.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2024 |
| Descrizione fisica | 1 online resource (663 pages) |
| Disciplina | 511.5 |
| Altri autori (Persone) |
SchweserThomas
ToftBjarne |
| Collana | Springer Monographs in Mathematics |
| Soggetto topico |
Graph theory
Graph Theory |
| ISBN | 3-031-50065-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Degree Bounds for the Chromatic Number -- 2 Degeneracy and Colorings -- 3 Colorings and Orientations of Graphs -- 4 Properties of Critical Graphs -- 5 Critical Graphs with few Edges -- 6 Bounding χ by ∆ and ω -- 7 Coloring of Hypergraphs -- 8 Homomorphisms and Colorings -- 9 Coloring Graphs on Surface -- Appendix A: Brooks’ Fundamental Paper -- Appendix B: Tutte’s Lecture from 1992 -- Appendix C: Basic Graph Theory Concepts. |
| Record Nr. | UNINA-9910845082203321 |
Stiebitz Michael
|
||
| Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2024 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Graph coloring problems / / Tommy R. Jensen, Bjarne Toft
| Graph coloring problems / / Tommy R. Jensen, Bjarne Toft |
| Autore | Jensen Tommy R. |
| Pubbl/distr/stampa | New York, New York : , : John Wiley & Sons, Inc., , 1995 |
| Descrizione fisica | 1 online resource (324 p.) |
| Disciplina |
511.5
511/.5 |
| Collana | Wiley-Interscience Series in Discrete Mathematics and Optimization |
| Soggetto topico | Graph coloring |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-33198-5
9786613331984 1-118-03249-7 1-118-03074-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Graph Coloring Problems; Contents; Preface; 1 Introduction to Graph Coloring; 1.1 Basic Definitions; 1.2 Graphs on Surfaces; 1.3 Vertex Degrees and Colorings; 1.4 Criticality and Complexity; 16.14 Partition Problem of Galvin and Hajnal; 1.5 Sparse Graphs and Random Graphs; 1.6 Perfect Graphs; 1.7 Edge-Coloring; 1.8 Orientations and Integer Flows; 1.9 List Coloring; 1.10 Generalized Graph Coloring; 1.11 Final Remarks; Bibliography; 2 Planar Graphs; 2.1 Four-Color Theorem; 2.2 Cartesian Sequences; 2.3 Intersection Graphs of Planar Segments; 2.4 Ringerl's Earth-Moon Problem
2.5 Ore and Plummer's Cyclic Chromatic Number2.6 Vertex Partitionings w.r.t. Coloring Number; 2.7 Vertex Partitionings w.r.t. Maximum Degree; 2.8 The Three-Color Problem; 2.9 Steinberg's Three-Color Problem; 2.10 Grünbaum and Havel's Three-Color Problem; 2.11 Grötzsch and Sachs' Three-Color Problem; 2.12 Barnette's Conjecture; 2.13 List-Coloring Planar Graphs; 2.14 Kronk and Mitchem's Entire Chromatic Number; 2.15 Nine-Color Conjecture; 2.16 Uniquely Colorable Graphs; 2.17 Density of 4-Critical Planar Graphs; 2.18 Square of Planar Graphs; Bibliography; 3 Graphs on Higher Surfaces 3.1 Heawood's Empire Problem3.2 Grünbaum's 3-Edge-Color Conjecture; 3.3 Albertson's Four-Color Problem; 3.4 Improper Colorings; 3.5 Number of 6-Critical Graphs on a Surface; 3.6 Toroidal Polyhedra; 3.7 Polynomial Coloring of Embedded Graphs; 3.8 Sparse Embedded Graphs; 3.9 Ringel's 1-Chromatic Number; 3.10 Borodin's Conjecture on Diagonal Coloring; 3.11 Acyclic Colorings; 3.12 Cochromatic Numbers; 3.13 Graphs on Pseudo-Surfaces; Bibliography; 4 Degrees; 4.1 The Coloring Number; 4.2 Coloring of Decomposable Graphs; 4.3 Color-Bound Families of Graphs; 4.4 Edge-Disjoint Placements 4.5 Powers of Hamilton Cycles4.6 Brooks' Theorem for Triangle-Free Graphs; 4.7 Graphs Without Large Complete Subgraphs; 4.8 k-Chromatic Graphs of Maximum Degree k; 4.9 Total Coloring; 4.10 Equitable Coloring; 4.11 Acyclic Coloring; 4.12 Melnikov's Valency-Variety Problem; 4.13 Induced-Odd Degree Subgraphs; 4.14 Strong Chromatic Number; Bibliography; 5 Critical Graphs; 5.1 Critical Graphs With Many Edges; 5.2 Minimum Degree of 4- and 5-Critical Graphs; 5.3 Critical Graphs With Few Edges; 5.4 Four-Critical Amenable Graphs; 5.5 Four-Critical Degree 5 Problem 5.6 Large Critical Subgraphs of Critical Graphs5.7 Critical Subgraph Covering a 2-Path; 5.8 Noninduced Critical Subgraphs; 5.9 Number of Critical Subgraphs; 5.10 Subgraphs of Critical Graphs; 5.11 Minimal Circumference of Critical Graphs; 5.12 The Erdös-Lovász Tihany Problem; 5.13 Partial Joins of Critical Graphs; 5.14 Vertex-Critical Graphs Without Critical Edges; Bibliography; 6 The Conjectures of Hadwiger and Hajós; 6.1 Hadwiger's Conjecture; 6.2 Hajós' Conjecture; 6.3 The (m, n)- and [m, n]-Conjectures; 6.4 Hadwiger Degree of a Graph; 6.5 Graphs Without Odd-K5; 6.6 Scheme Conjecture 6.7 Chromatic 4-Schemes |
| Record Nr. | UNINA-9910141196003321 |
|
Jensen Tommy R.
|
||
| New York, New York : , : John Wiley & Sons, Inc., , 1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Graph coloring problems / / Tommy R. Jensen, Bjarne Toft
| Graph coloring problems / / Tommy R. Jensen, Bjarne Toft |
| Autore | Jensen Tommy R. |
| Pubbl/distr/stampa | New York, New York : , : John Wiley & Sons, Inc., , 1995 |
| Descrizione fisica | 1 online resource (324 p.) |
| Disciplina |
511.5
511/.5 |
| Collana | Wiley-Interscience Series in Discrete Mathematics and Optimization |
| Soggetto topico | Graph coloring |
| ISBN |
1-283-33198-5
9786613331984 1-118-03249-7 1-118-03074-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Graph Coloring Problems; Contents; Preface; 1 Introduction to Graph Coloring; 1.1 Basic Definitions; 1.2 Graphs on Surfaces; 1.3 Vertex Degrees and Colorings; 1.4 Criticality and Complexity; 16.14 Partition Problem of Galvin and Hajnal; 1.5 Sparse Graphs and Random Graphs; 1.6 Perfect Graphs; 1.7 Edge-Coloring; 1.8 Orientations and Integer Flows; 1.9 List Coloring; 1.10 Generalized Graph Coloring; 1.11 Final Remarks; Bibliography; 2 Planar Graphs; 2.1 Four-Color Theorem; 2.2 Cartesian Sequences; 2.3 Intersection Graphs of Planar Segments; 2.4 Ringerl's Earth-Moon Problem
2.5 Ore and Plummer's Cyclic Chromatic Number2.6 Vertex Partitionings w.r.t. Coloring Number; 2.7 Vertex Partitionings w.r.t. Maximum Degree; 2.8 The Three-Color Problem; 2.9 Steinberg's Three-Color Problem; 2.10 Grünbaum and Havel's Three-Color Problem; 2.11 Grötzsch and Sachs' Three-Color Problem; 2.12 Barnette's Conjecture; 2.13 List-Coloring Planar Graphs; 2.14 Kronk and Mitchem's Entire Chromatic Number; 2.15 Nine-Color Conjecture; 2.16 Uniquely Colorable Graphs; 2.17 Density of 4-Critical Planar Graphs; 2.18 Square of Planar Graphs; Bibliography; 3 Graphs on Higher Surfaces 3.1 Heawood's Empire Problem3.2 Grünbaum's 3-Edge-Color Conjecture; 3.3 Albertson's Four-Color Problem; 3.4 Improper Colorings; 3.5 Number of 6-Critical Graphs on a Surface; 3.6 Toroidal Polyhedra; 3.7 Polynomial Coloring of Embedded Graphs; 3.8 Sparse Embedded Graphs; 3.9 Ringel's 1-Chromatic Number; 3.10 Borodin's Conjecture on Diagonal Coloring; 3.11 Acyclic Colorings; 3.12 Cochromatic Numbers; 3.13 Graphs on Pseudo-Surfaces; Bibliography; 4 Degrees; 4.1 The Coloring Number; 4.2 Coloring of Decomposable Graphs; 4.3 Color-Bound Families of Graphs; 4.4 Edge-Disjoint Placements 4.5 Powers of Hamilton Cycles4.6 Brooks' Theorem for Triangle-Free Graphs; 4.7 Graphs Without Large Complete Subgraphs; 4.8 k-Chromatic Graphs of Maximum Degree k; 4.9 Total Coloring; 4.10 Equitable Coloring; 4.11 Acyclic Coloring; 4.12 Melnikov's Valency-Variety Problem; 4.13 Induced-Odd Degree Subgraphs; 4.14 Strong Chromatic Number; Bibliography; 5 Critical Graphs; 5.1 Critical Graphs With Many Edges; 5.2 Minimum Degree of 4- and 5-Critical Graphs; 5.3 Critical Graphs With Few Edges; 5.4 Four-Critical Amenable Graphs; 5.5 Four-Critical Degree 5 Problem 5.6 Large Critical Subgraphs of Critical Graphs5.7 Critical Subgraph Covering a 2-Path; 5.8 Noninduced Critical Subgraphs; 5.9 Number of Critical Subgraphs; 5.10 Subgraphs of Critical Graphs; 5.11 Minimal Circumference of Critical Graphs; 5.12 The Erdös-Lovász Tihany Problem; 5.13 Partial Joins of Critical Graphs; 5.14 Vertex-Critical Graphs Without Critical Edges; Bibliography; 6 The Conjectures of Hadwiger and Hajós; 6.1 Hadwiger's Conjecture; 6.2 Hajós' Conjecture; 6.3 The (m, n)- and [m, n]-Conjectures; 6.4 Hadwiger Degree of a Graph; 6.5 Graphs Without Odd-K5; 6.6 Scheme Conjecture 6.7 Chromatic 4-Schemes |
| Record Nr. | UNISA-996199059103316 |
|
Jensen Tommy R.
|
||
| New York, New York : , : John Wiley & Sons, Inc., , 1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Graph coloring problems / / Tommy R. Jensen, Bjarne Toft
| Graph coloring problems / / Tommy R. Jensen, Bjarne Toft |
| Autore | Jensen Tommy R. |
| Pubbl/distr/stampa | New York, New York : , : John Wiley & Sons, Inc., , 1995 |
| Descrizione fisica | 1 online resource (324 p.) |
| Disciplina |
511.5
511/.5 |
| Collana | Wiley-Interscience Series in Discrete Mathematics and Optimization |
| Soggetto topico | Graph coloring |
| ISBN |
1-283-33198-5
9786613331984 1-118-03249-7 1-118-03074-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Graph Coloring Problems; Contents; Preface; 1 Introduction to Graph Coloring; 1.1 Basic Definitions; 1.2 Graphs on Surfaces; 1.3 Vertex Degrees and Colorings; 1.4 Criticality and Complexity; 16.14 Partition Problem of Galvin and Hajnal; 1.5 Sparse Graphs and Random Graphs; 1.6 Perfect Graphs; 1.7 Edge-Coloring; 1.8 Orientations and Integer Flows; 1.9 List Coloring; 1.10 Generalized Graph Coloring; 1.11 Final Remarks; Bibliography; 2 Planar Graphs; 2.1 Four-Color Theorem; 2.2 Cartesian Sequences; 2.3 Intersection Graphs of Planar Segments; 2.4 Ringerl's Earth-Moon Problem
2.5 Ore and Plummer's Cyclic Chromatic Number2.6 Vertex Partitionings w.r.t. Coloring Number; 2.7 Vertex Partitionings w.r.t. Maximum Degree; 2.8 The Three-Color Problem; 2.9 Steinberg's Three-Color Problem; 2.10 Grünbaum and Havel's Three-Color Problem; 2.11 Grötzsch and Sachs' Three-Color Problem; 2.12 Barnette's Conjecture; 2.13 List-Coloring Planar Graphs; 2.14 Kronk and Mitchem's Entire Chromatic Number; 2.15 Nine-Color Conjecture; 2.16 Uniquely Colorable Graphs; 2.17 Density of 4-Critical Planar Graphs; 2.18 Square of Planar Graphs; Bibliography; 3 Graphs on Higher Surfaces 3.1 Heawood's Empire Problem3.2 Grünbaum's 3-Edge-Color Conjecture; 3.3 Albertson's Four-Color Problem; 3.4 Improper Colorings; 3.5 Number of 6-Critical Graphs on a Surface; 3.6 Toroidal Polyhedra; 3.7 Polynomial Coloring of Embedded Graphs; 3.8 Sparse Embedded Graphs; 3.9 Ringel's 1-Chromatic Number; 3.10 Borodin's Conjecture on Diagonal Coloring; 3.11 Acyclic Colorings; 3.12 Cochromatic Numbers; 3.13 Graphs on Pseudo-Surfaces; Bibliography; 4 Degrees; 4.1 The Coloring Number; 4.2 Coloring of Decomposable Graphs; 4.3 Color-Bound Families of Graphs; 4.4 Edge-Disjoint Placements 4.5 Powers of Hamilton Cycles4.6 Brooks' Theorem for Triangle-Free Graphs; 4.7 Graphs Without Large Complete Subgraphs; 4.8 k-Chromatic Graphs of Maximum Degree k; 4.9 Total Coloring; 4.10 Equitable Coloring; 4.11 Acyclic Coloring; 4.12 Melnikov's Valency-Variety Problem; 4.13 Induced-Odd Degree Subgraphs; 4.14 Strong Chromatic Number; Bibliography; 5 Critical Graphs; 5.1 Critical Graphs With Many Edges; 5.2 Minimum Degree of 4- and 5-Critical Graphs; 5.3 Critical Graphs With Few Edges; 5.4 Four-Critical Amenable Graphs; 5.5 Four-Critical Degree 5 Problem 5.6 Large Critical Subgraphs of Critical Graphs5.7 Critical Subgraph Covering a 2-Path; 5.8 Noninduced Critical Subgraphs; 5.9 Number of Critical Subgraphs; 5.10 Subgraphs of Critical Graphs; 5.11 Minimal Circumference of Critical Graphs; 5.12 The Erdös-Lovász Tihany Problem; 5.13 Partial Joins of Critical Graphs; 5.14 Vertex-Critical Graphs Without Critical Edges; Bibliography; 6 The Conjectures of Hadwiger and Hajós; 6.1 Hadwiger's Conjecture; 6.2 Hajós' Conjecture; 6.3 The (m, n)- and [m, n]-Conjectures; 6.4 Hadwiger Degree of a Graph; 6.5 Graphs Without Odd-K5; 6.6 Scheme Conjecture 6.7 Chromatic 4-Schemes |
| Record Nr. | UNINA-9910830671103321 |
|
Jensen Tommy R.
|
||
| New York, New York : , : John Wiley & Sons, Inc., , 1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||