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Large Networks and Graph Limits

About this Title

László Lovász, Eötvös Loránd University, Budapest, Hungary

Publication: Colloquium Publications
Publication Year: 2012; Volume 60
ISBNs: 978-0-8218-9085-1 (print); 978-1-4704-1583-9 (online)
DOI: https://doi.org/10.1090/coll/060
MathSciNet review: MR3012035
MSC: Primary 05-02; Secondary 05C60, 05C80, 05C82, 05D40

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Table of Contents

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Front/Back Matter

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Part 1. Large graphs: An informal introduction

• Chapter 1. Very large networks
• Chapter 2. Large graphs in mathematics and physics

Part 2. The algebra of graph homomorphisms

• Chapter 3. Notation and terminology
• Chapter 4. Graph parameters and connection matrices
• Chapter 5. Graph homomorphisms
• Chapter 6. Graph algebras and homomorphism functions

Part 3. Limits of dense graph sequences

• Chapter 7. Kernels and graphons
• Chapter 8. The cut distance
• Chapter 9. Szemerédi partitions
• Chapter 10. Sampling
• Chapter 11. Convergence of dense graph sequences
• Chapter 12. Convergence from the right
• Chapter 13. On the structure of graphons
• Chapter 14. The space of graphons
• Chapter 15. Algorithms for large graphs and graphons
• Chapter 16. Extremal theory of dense graphs
• Chapter 17. Multigraphs and decorated graphs

Part 4. Limits of bounded degree graphs

• Chapter 18. Graphings
• Chapter 19. Convergence of bounded degree graphs
• Chapter 20. Right convergence of bounded degree graphs
• Chapter 21. On the structure of graphings
• Chapter 22. Algorithms for bounded degree graphs

Part 5. Extensions: A brief survey

• Chapter 23. Other combinatorial structures
• Appendix A