# Questions tagged [ramsey-theory]

Branch of combinatorics with the philosophy that 'total disorder is impossible'. For example, Ramsey's theorem asserts that for each $n$, every sufficiently large graph either contains a clique of size $n$ or a stable set of size $n$.

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### Convex pigeonhole principle in Banach spaces

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### Original Paper for "Bipartite Ramsey Theory" by Hattingh, Johannes H, 1998

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### Happy ending problem – Why not a proof by induction?

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### Roelcke precompactness and Ramsey property

**4**

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### Ramsey style theorem with unbounded colors

**4**

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### The number of monochromatic triangles

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### Well approximating sets

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### A question on Borel equivalence relations

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### Equal subset-sums of bounded vectors

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### Best known upper bound for the Ramsey function $R(k,x)$

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### Ramsey Numbers for Integers

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### Graphs with linear Ramsey number for two colors, but super-linear Ramsey number for three colors?

**2**

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### The extension of the substitution map of the semigroup of variable words to its Stone–Čech compactification is a homomorphism

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### Primitive recursive bounds for the the Gallai-Witt theorem

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### Density of Ramsey subsets of $\omega$

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### A generalization of Hales-Jewett theorem

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### Quantitative Ramsey theorem - asymmetric and multicolors

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### Computation of cyclic van der Waerden numbers

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### Independence number of $C_4$-free graphs

**3**

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### Ramsey´s number R(4,4) with arithmetic progressions

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### Ron L. Graham’s lesser known significant contributions

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### Lower bound for diagonal Ramsey numbers —- reference request

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### Ramsey theory in infinite-dimensional projective spaces

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### Additivity of the upper Banach density

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### Ramsey graph for C4 graph

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### 3 term van der Waerden with large step size

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### Is Green-Tao's theorem a consequence of Van der Waerden theorem?

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### Ramsey-Kuratowski numbers

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### Counting progressions for Ramsey-type number

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### Ramsey type properties of $F_\sigma$ ideals

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### Is there a known proof that $R(5,5)\leq 47$ in Ramsey theory?

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### If $S_\mathbb N$ is partitioned into finitely many pieces, must one piece contain a "skew copy" of every countable group?

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### Winning strategies for a game on the natural numbers

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### An analytic game and Ramsey's theorem

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### Games and Ramsey's theorem

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### Consistency of a tighter bound than given by Erdős–Rado in a special case

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### Coloring triples in trees

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### Consequences of Ramsey-numbers of hypergraphs

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### Is the Upper Banach density always zero with respect to some sequence of Finite subset

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### Metrically Ramsey ultrafilters

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### Induction on the number of edges $(-1)^wI(G)\leq (-1)^w\sum_{i=0}^w(-1)^ig_i.$

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### Does every bijective graph endomorphism restrict to a full-cardinality isomorphism?

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### Partition Calculus and Ramsey theory question

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### Looking for “Set theory for a small universe” by Ketonen

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### The set of homogeneous solutions of a clopen contains an hyperarithmetical set

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### A combinatorial property of uncountable groups, II

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### A combinatorial property of uncountable groups

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### $R(3,6) = 18$, especially proving that $R(3,6)>17$

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### monochromatic induced subgraph in a complete 3-partite graph

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