Graph Colorings.

Intro -- Contents -- Preface -- Graph coloring -- History of graph coloring -- Models of graph coloring -- Preface to the English Edition -- Chapter 1. Classical Coloring of Graphs -- 1.1. Basic terms and definitions -- 1.2. Classical vertex-coloring -- 1.3. Classical edge-coloring -- Chapter 2. On-line Coloring of Graphs -- 2.1. On-line and off-line coloring -- 2.2. On-line coloring algorithms -- 2.3. Worst case effectiveness of on-line coloring -- 2.4. Expected effectiveness of on-line coloring -- 2.5. Susceptibility of graphs -- 2.6. Coloring of intersection graphs -- 2.7. Applications to resource management -- Chapter 3. Equitable Coloring of Graphs -- 3.1. Equitable vertex-coloring -- 3.2. Equitable total coloring -- Chapter 4. Sum Coloring of Graphs -- 4.1. Definition and simple properties -- 4.2. The complexity of the sum coloring problem -- 4.3. Generalizations of the sum coloring problem -- 4.4. Some applications of the sum coloring problem -- Chapter 5. T-Coloring of Graphs -- 5.1. The spans -- 5.2. Sets of forbidden distances -- 5.3. T-colorings of graphs -- 5.4. T-spans and T-chromatic numbers -- 5.5. Homomorphisms and T-graphs -- 5.6. Estimates and exact values -- 5.7. The computational complexity -- 5.8. Approximation algorithms -- 5.9. Applications -- Chapter 6. Rank Coloring of Graphs -- 6.1. Vertex ranking -- 6.2. Edge ranking -- Chapter 7. Harmonious Coloring of Graphs -- 7.1. Introduction -- 7.2. Graphs with known harmonious number -- 7.3. Bounds for the harmonious chromatic number of general graphs -- 7.4. Algorithm Depressive -- 7.5. Applications -- Chapter 8. Interval Edge-Coloring of Graphs -- 8.1. Basic properties of the model -- 8.2. Consecutively colorable bipartite graphs -- 8.3. The span of interval coloring -- 8.4. Deficiency of graphs -- Chapter 9. Circular Coloring of Graphs.

9.1. Circular coloring of the vertices of a graph -- 9.2. Circular coloring of the edges of a graph -- Chapter 10. Path Coloring and Routing in Graphs -- 10.1. Basic definitions -- 10.2. Known results -- 10.3. Applications -- Chapter 11. List Colorings of Graphs -- 11.1. Notation and definitions -- 11.2. Bipartite and 2-choosable graphs -- 11.3. The Hajós Construction -- 11.4. D-choosability and Brooks theorem -- 11.5. Planar graphs -- 11.6. Graphs for which X = Xι -- 11.7. (k, r)-choosability -- 11.8. Edge-list coloring -- Chapter 12. Ramsey Colorings of Complete Graphs -- 12.1. Notation and basic definitions -- 12.2. Ramsey numbers -- 12.3. Values and properties of classical Ramsey numbers -- 12.4. Nonclassical Ramsey numbers -- 12.5. Applications of Ramsey numbers -- Chapter 13. Placing Guards in Art Galleries by Graph Coloring -- 13.1. Introduction -- 13.2. Fisk's proof -- 13.3. The orthogonal art gallery theorem -- 13.4. Orthogonal polygons with holes -- 13.5. Final remarks -- Bibliography -- Index -- Authors' addresses.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.