The Girth Ramsey Theorem by Christian Reiher
An introduction to structural Ramsey theory that builds to a resolution of one of its long-standing conjectures
Structural Ramsey theory is an area of combinatorics about Ramsey-type statements dealing with hypergraphs as well as other combinatorial structures. Rather than mainly focusing on numerical aspects such as Ramsey numbers, structural Ramsey theory focuses on the existence of Ramsey-type statements and their connection with some other fields of mathematics. In this book, Christian Reiher and Vojtěch Rödl introduce structural Ramsey theory and solve a long-standing problem regarding locally sparse Ramsey graphs.
The book has two parts. The first part, which is suitable for a topics course, introduces tools used in the construction of locally sparse Ramsey graphs and hypergraphs, and covers several well-known results, such as Ramsey’s theorem and the Hales-Jewett theorem. The focus is on structural Ramsey theory of hypergraphs and on the introduction of partite construction, which is illustrated by several of its applications yielding the proof of some older results in the area. The second part establishes the girth Ramsey theorem, resolving a decades’ old conjecture in structural Ramsey theory implying that for every graph G and every number of colors, there exists a Ramsey graph H with girth(H) = girth(G).
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Riemann Surfaces and Related Topics
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Seminar on the Atiyah-Singer Index Theorem
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Moments, Monodromy, and Perversity
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The Master Equation and the Convergence Problem in Mean Field Games
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Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations
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Lectures on Curves on an Algebraic Surface
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Intermittent Convex Integration for the 3D Euler Equations
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Instability and Non-uniqueness for the 2D Euler Equations, after M. Vishik
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The Einstein-Klein-Gordon Coupled System
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A Hierarchy of Turing Degrees
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Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems
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Dynamics in One Complex Variable
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Elementary Differential Topology
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An Introduction to G-Functions
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Some Problems of Unlikely Intersections in Arithmetic and Geometry
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The Norm Residue Theorem in Motivic Cohomology
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The Structure of Groups with a Quasiconvex Hierarchy
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Lectures on P-Adic L-Functions
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Curvature and Betti Numbers
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Radically Elementary Probability Theory
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Period Spaces for p-divisible Groups
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Exponential Sums and Differential Equations
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Functional Operators, Volume 2
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Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom
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The Decomposition of Global Conformal Invariants
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Classification of Pseudo-reductive Groups
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Weyl Group Multiple Dirichlet Series
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Green's Function Estimates for Lattice Schroedinger Operators and Applications. (AM-158)
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Automata Studies
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Arithmetic and Geometry
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Stationary Processes and Prediction Theory
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Arithmetic Moduli of Elliptic Curves
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Flows on Homogeneous Spaces
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Seminar on Singularities of Solutions of Linear Partial Differential Equations
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Functional Operators, Volume 1
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Contributions to Fourier Analysis
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Unipotent Ideals and Harish-Chandra Bimodules
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Hoelder Continuous Euler Flows in Three Dimensions with Compact Support in Time
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Non-Archimedean Tame Topology and Stably Dominated Types
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The p-adic Simpson Correspondence
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The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures
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Contributions to the Theory of Games, Volume IV
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Seminar on Micro-Local Analysis
| SKU | Unavailable |
| ISBN 13 | 9780691280950 |
| ISBN 10 | 0691280959 |
| Title | The Girth Ramsey Theorem |
| Author | Christian Reiher |
| Series | Annals Of Mathematics Studies |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Princeton University Press |
| Year published | 2027-02-16 |
| Number of pages | 206 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |