UID:
almafu_9958090790702883
Umfang:
1 online resource (277 p.)
ISBN:
1-281-76639-9
,
9786611766399
,
0-08-087339-1
Serie:
Pure and applied mathematics; a series of monographs and textbooks ; 27
Inhalt:
The four-color problem
Anmerkung:
Description based upon print version of record.
,
Front Cover; The Problem Four-Color, Volume 27; Copyright Page; Contents; Preface; Introduction; Chapter 1. Planar Graphs; 1.1. Planar Representations; 1.2. The Faces; 1.3. Maximal Planar Graphs. Straight Line Representations; Chapter 2. Bridges and Circuits; 2.1. Bridges in General Graphs; 2.2. Circuit Bridges; 2.3. Equivalence of Planar Representations; 2.4. Uniqueness of Representations; 2.5. Transfer of Bridges; 2.6. Characterization of Planar Graphs; 2.7. Further Observations on Maximal Graphs; Chapter 3. Dual Graphs; 3.1. Geometric Definition of Duality
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3.2. Observations on Graphs and Their Duals3.3. Relational Definition of Duality; 3.4. Characterization of Planar Graphs; 3.5. Maximal Bipartite Graphs. Self-Dual Graphs; Chapter 4. Euler's Formula and Its Consequences; 4.1. Euler's Formula; 4.2. Regular Graphs; 4.3. The Euler Contributions; Chapter 5. Large Circuits; 5.1. Circuit Arcs; 5.2. Hamilton Circuits; Chapter 6. Colorations; 6.1. Types of Coloration; 6.2. Two Colors; 6.3. Reductions; 6.4. The Five-Color Theorem; 6.5. TheTheorem of Brooks; Chapter 7. Color Functions; 7.1. Vertex Coloration; 7.2. The Dual Theory
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7.3. Color Directed Graphs7.4. Some Special Applications; Chapter 8. Formulations of the Four-Color Problem; 8.1. Decomposition into Three Subgraphs; 8.2. Bipartite Dichotomy; 8.3. Even Subgraphs; 8.4. Graphs with Small Face Boundaries; 8.5. Angle Characters and Congruence Conditions (mod 3); Chapter 9. Cubic Graphs; 9.1. Color Reduction to Cubic Graphs; 9.2. Configurations in Cubic Graphs; 9.3. Four-Color Conditions in Cubic Graphs; 9.4. The Interchange Graph and the Color Problems; 9.5. Planar Interchange Graphs; 9.6. Construction of Cubic Graphs; Chapter 10. Hadwiger's Conjecture
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10.1. Contractions and Subcontractions10.2. Maximal Graphs and Simplex Decompositions; 10.3. lndecomposable Graphs; 10.4. Hadwiger's Conjecture; 10.5. Wagner's Equivalence Theorem; 10.6. Contractions to S4; 10.7. Multiply-Connected Graphs; Chapter 11. Critical Graphs; 11.1. Types of Critical Graphs; 11.2. Contraction Critical Graphs; 11.3. Edge-Critical Graphs; 11. 4. Construction of e-Critical Graphs; 11.5. Conjunctions and Mergers; 11.6. Amalgamations; 11. 7. Mergers of Simplexes; Chapter 12. Planar 5-Chromatic Graphs; 12.1. Separations; 12.2. Irreducible Graphs
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12.3. Reductions for Minor Vertices12.4. Errera Circuits and 5-Components; 12.5. Lower Bounds for Irreducible Graphs; Chapter 13. Three Colors; 13.1. Formulations of the Three-Color Problem; 13.2. The Theorem of Grötzsch; Chapter 14. Edge Coloration; 14.1. General Observations; 14.2. Coloration of an Augmented Graph; 14.3. The Theorem ofShannon; 14.4. The Theorem of Vizing; Bibliography; Author Index; Subject Index
,
English
Weitere Ausg.:
ISBN 0-12-374571-3
Sprache:
Englisch
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