Planar Graphs. Graphs on Higher Surfaces. Degrees. Critical Graphs. The Conjectures of Hadwiger and Hajos. Sparse Graphs. Perfect Graphs. Geometric and Combinatorial Graphs. Algorithms. Constructions. Edge Colorings. Orientations and Flows. Chromatic Polynomials. Hypergraphs. Infinite Chromatic Graphs. Miscellaneous Problems. Indexes.

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Graph Coloring Problems

Introduction 1. Examples and basic concepts 2. Topological dynamics 3. Symbolic dynamics 4. Ergodic theory 5. Hyperbolic dynamics 6. Ergodicity of Anosov diffeomorphisms 7. Low-dimensional dynamics 8. Complex dynamics 9. Measure-theoretic entropy Bibliography Index.

http://catdir.loc.gov/catdir/samples/cam033/2002022281.pdf

Introduction to dynamical systems

Finite sums from sequences within cells of a partition of N

(A) In this paper we study some connections between the Fraisse theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism groups of countable structures. A prime concern of topological dynamics is the study of continuous actions of (Hausdorff) topological groups G on (Hausdorff) compact spaces X.

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Fraïssé Limits, Ramsey Theory, and topological dynamics of automorphism groups

We study in this paper some connections between the Fraisse theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism groups of countable structures.

Fraisse Limits, Ramsey Theory, and Topological Dynamics of Automorphism Groups

/pdf/ramsey-s-theorem-for-n-parameter-sets-41of2mwzbk.pdf

Ramsey’s theorem for $n$-parameter sets

Ramsey's theorem for a class of categories

Recently a number of striking new results have been proved in an area becoming known as Ramsey Theory. It is our purpose here to describe some of these. Ramsey Theory is a part of combinatorial mathematics dealing with assertions of a certain type, which we will indicate below. Among the earliest theorems of this type are Ramsey’s theorem, of course, Van Der Waerden’s theorem on arithmetic progressions and Schur’s theorem on solutions of x+y = z.

Some Recent Developments in Ramsey Theory

In this paper we present a Ramsey theorem for certain categories which is sufficiently general to include as special cases the finite vector space analog to Ramsey’s theorem (conjectured by Gian-Carlo Rota), the Ramsey theorem for n-parameter sets [21, as well as Ramsey’s theorem itself [4, 61. The Ramsey theorem for finite affine spaces is obtained here simultaneously with that for vector spaces. That these two are equivalent was already known [5, II, and the arguments previously used to show that the affine theorem implies the projective theorem are also special cases of the results of this paper.

B. L. Rothschild

Papers

Ramsey’s theorem for $n$-parameter sets

Ramsey's theorem for a class of categories

Some Recent Developments in Ramsey Theory

Ramsey's Theorem for a Class of Categories.