| Description |
1 online resource |
| Series |
Springer monographs in mathematics, 1439-7382 |
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Springer monographs in mathematics.
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| Contents |
880-01 Introduction -- Research Method -- Major Attributes of Project Performance -- Critical Success Factors for Projects -- Project Performance Prediction -- Success Traits for a Construction Project -- Project Coordination for Success -- Other Issues in Project Coordination and Traits of a Project Coordinator -- Summary and Conclusions |
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880-01/(S Machine generated contents note: 1. Introduction -- 1.1. Introduction -- 1.2. Total Dominating Set in a Graph -- 1.3. Graph Theory Terminology and Concepts -- 1.4. Digraph Terminology and Concepts -- 1.5. Hypergraph Terminology and Concepts -- 1.6. Transition from Total Domination in Graphs to Transversals in Hypergraphs -- 2. Properties of Total Dominating Sets and General Bounds -- 2.1. Introduction -- 2.2. Properties of Total Dominating Sets -- 2.3. General Bounds -- 2.3.1. Bounds in Terms of the Order -- 2.3.2. Bounds in Terms of the Order and Size -- 2.3.3. Bounds in Terms of Maximum Degree -- 2.3.4. Bounds in Terms of Radius and Diameter -- 2.3.5. Bounds in Terms of Girth -- 2.4. Bounds in Terms of the Domination Number -- 3. Complexity and Algorithmic Results -- 3.1. Introduction -- 3.2. Complexity -- 3.2.1. Time Complexities -- 3.3. Fixed Parameter Tractability -- 3.4. Approximation Algorithms -- 3.5. Tree Algorithm -- 3.6. Simple Heuristic -- 4. Total Domination in Trees -- 4.1. Introduction -- 4.2. Bounds on the Total Domination Number in Trees -- 4.3. Total Domination and Open Packings -- 4.4. Vertices Contained in All, or in No, Minimum TD-Sets -- 4.5. Trees with Unique Minimum TD-Sets -- 4.6. Trees T with γt (T) = 2γ(T) -- 4.7. Trees with γt(T) = γ(T) -- 5. Total Domination and Minimum Degree -- 5.1. Introduction -- 5.2. General Bound Involving Minimum Degree -- 5.3. Minimum Degree One -- 5.4. Minimum Degree Two -- 5.5. Minimum Degree Three -- 5.6. Minimum Degree Four -- 5.7. Minimum Degree Five -- 5.8. Summary of Known Results on Bounds in Terms of Order -- 5.9. Total Domination and Connectivity -- 6. Total Domination in Planar Graphs -- 6.1. Introduction -- 6.2. Diameter Two Planar Graphs -- 6.3. Diameter Three Planar Graphs -- 7. Total Domination and Forbidden Cycles -- 7.1. Introduction -- 7.2. Forbidden 6-Cycles -- 7.3. Total Domination and Girth -- 8. Relating the Size and Total Domination Number -- 8.1. Introduction -- 8.2. Relating the Size and Total Domination Number -- 9. Total Domination in Claw-Free Graphs -- 9.1. Introduction -- 9.2. Minimum Degree One -- 9.3. Minimum Degree Two -- 9.4. Cubic Graphs -- 10. Total Domination Number Versus Matching Number -- 10.1. Introduction -- 10.2. Relating the Total Domination and Matching Numbers -- 10.3. Graphs with Total Domination Number at Most the Matching Number -- 10.3.1. Claw-Free Graphs -- 10.3.2. Regular Graphs -- 10.3.3. Graphs with Every Vertex in a Triangle -- 11. Total Domination Critical Graphs -- 11.1. Introduction -- 11.2. Total Domination Edge-Critical Graphs -- 11.2.1. Supercritical Graphs -- 11.2.2. General Constructions -- 11.2.3. Diameter of γτEC Graphs -- 11.2.4. Applications to Diameter-2-Critical Graphs -- 11.2.5. Total Domination Vertex-Critical Graphs -- 11.2.6. γτVC Graphs of High Connectivity -- 11.3. Total Domination Edge Addition Stable Graphs -- 11.4. Total Domination Edge Removal Stable Graphs -- 11.5. Total Domination Vertex Removal Changing Graphs -- 11.6. Total Domination Vertex Removal Stable Graphs -- 12. Total Domination and Graph Products -- 12.1. Introduction -- 12.2. Cartesian Product -- 12.3. Direct Product -- 13. Graphs with Disjoint Total Dominating Sets -- 13.1. Introduction -- 13.2. Augmenting a Graph -- 13.3. Disjoint Dominating and Total Dominating Sets -- 13.4. Dominating and Total Dominating Partitions in Cubic Graphs -- 13.5. Surprising Relationship -- 14. Total Domination in Graphs with Diameter Two -- 14.1. Introduction -- 14.2. Preliminary Observations -- 14.3. Diameter-2 Moore Graphs -- 14.4. Optimal Upper Bound -- 15. Nordhaus-Gaddum Bounds for Total Domination -- 15.1. Introduction -- 15.2. Nordhaus-Gaddum Bounds for Total Domination -- 15.3. Total Domination Number and Relative Complement -- 15.4. Multiple Factor Nordhaus-Gaddum-Type Results -- 16. Upper Total Domination -- 16.1. Upper Total Domination -- 16.1.1. Trees -- 16.1.2. Upper Total Domination Versus Upper Domination -- 16.2. Bounds on the Upper Total Domination Number -- 16.3. Upper Total Domination in Claw-Free Graphs -- 16.4. Upper Total Domination in Regular Graphs -- 16.5. Vizing-Like Bound for Upper Total Domination -- 17. Variations of Total Domination -- 17.1. Introduction -- 17.2. Total Restrained Domination -- 17.3. Double Total Domination -- 17.4. Locating Total Domination -- 17.5. Differentiating Total Domination -- 18. Conjectures and Open Problems -- 18.1. Introduction -- 18.2. Total Domination Edge-Critical Graphs -- 18.3. Planar Graphs -- 18.4. C4-Free Graphs -- 18.5. Minimum Degree Four -- 18.6. Minimum Degree Five -- 18.7. Relating the Size and Total Domination Number -- 18.8. Augmenting a Graph -- 18.9. Dominating and Total Dominating Partitions in Cubic Graphs -- 18.10. Upper Total Domination Versus Upper Domination -- 18.11. Total Domination Vertex-Critical Graphs -- 18.12. Total Domination Number in Claw-Free Graphs -- 18.13. Total Domination Number and Distance -- 18.14. Total Domination Number and Relative Complement -- 18.15. Total Restrained Domination -- 18.16. Double Total Domination Number -- 18.17. Locating-Total Domination -- 18.18. Differentiating Total Domination -- 18.19. Graffiti Conjectures |
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Introduction -- Properties of Total Dominating Sets and General Bounds -- Complexity and Algorithmic Results -- Total Domination in Trees -- Total Domination and Minimum Degree -- Total Domination in Planar Graphs -- Total Domination and Forbidden Cycles -- Relating the Size and Total Domination Number -- Total Domination in Claw-Free Graphs -- Total Domination Number Versus Matching Number -- Total Domination Critical Graphs -- Total Domination and Graph Products -- Graphs with Disjoint Total Dominating Sets -- Total Domination in Graphs with Diameter Two -- Nordhaus-Gaddum Bounds for Total Domination -- Upper Total Domination -- Variations of Total Domination -- Conjectures and Open Problems |
| Summary |
Total Domination in Graphs gives a clear understanding of this topic to any interested reader who has a modest background in graph theory. This book provides and explores the fundamentals of total domination in graphs. Some of the topics featured include the interplay between total domination in graphs and transversals in hypergraphs, and the association with total domination in graphs and diameter-2-critical graphs. Several proofs are included in this text which enables readers to acquaint themselves with a toolbox of proof techniques and ideas with which to attack open problems in the field. This work is an excellent resource for students interested in beginning their research in this field. Additionally, established researchers will find the book valuable to have as it contains the latest developments and open problems |
| Analysis |
Mathematics |
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Global analysis (Mathematics) |
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Number theory |
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Graph Theory |
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Analysis |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
| Subject |
Domination (Graph theory)
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MATHEMATICS -- General.
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Teoría de grafos
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Domination (Graph theory)
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| Form |
Electronic book
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| Author |
Yeo, Anders
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| ISBN |
9781461465256 |
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1461465257 |
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