Results 21 to 30 of about 1,180 (130)
Reverse mathematics and infinite traceable graphs [PDF]
, 2010 This paper falls within the general program of investigating the proof theoretic strength (in terms of reverse mathematics) of combinatorial principals which follow from versions of Ramsey's theorem.
Cholak, Peter +2 more
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Advances in Mathematics, 1992 AbstractWe state and prove a theorem in exterior algebra which is an analogue of Ramsey's theorem in combinatorics, with vector spaces and alternating multilinear maps taking the roles played by sets and colorings. Our result can also be formulated as a theorem about the geometry of Grassmannians.
James Propp, David Feldman
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A multidimensional Ramsey Theorem
, 2022 Ramsey theory is a central and active branch of combinatorics. Although Ramsey numbers for graphs have been extensively investigated since Ramsey's work in the 1930s, there is still an exponential gap between the best known lower and upper bounds. For $k$-uniform hypergraphs, the bounds are of tower-type, where the height grows with $k$.
Antonio Girão +2 more
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Controlling iterated jumps of solutions to combinatorial problems [PDF]
, 2016 Among the Ramsey-type hierarchies, namely, Ramsey's theorem, the free set, the thin set and the rainbow Ramsey theorem, only Ramsey's theorem is known to collapse in reverse mathematics.
Patey, Ludovic
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Electronic Notes in Discrete Mathematics, 2017 8 pages, extended abstract for Eurocomb ...
Jan Hubička, Jaroslav Nešetřil
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Discrete Applied Mathematics, 1989 AbstractIn this paper we will consider Ramsey-type problems for finite graphs, r-partitions and hypergraphs. All these problems ask for the existence of large homogeneous (monochromatic) configurations of a certain kind under the condition that the size of the underlying set is large.
Andras Hajnal, Paul Erdős
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Journal of Combinatorial Theory, Series A, 1979 AbstractWe prove a Ramsey theorem for trees. The infinite version of this theorem can be stated: if T is a rooted tree of infinite height with each node of T having at least one but finitely many immediate successors, if n is a positive integer, and if the collection of all strongly embedded, height-n subtrees of T is partitioned into finitely many ...
Keith Robert Milliken +1 more
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A Model Theoretic Proof of Completeness of an Axiomatization of Monadic Second-Order Logic on Streams [PDF]
, 2012 International audienceWe discuss the completeness of an axiomatization of Monadic Second- Order Logic (MSO) on infinite words (or streams). By using model-theoretic tools, we give an alternative proof of D.
Riba, Colin
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Ramsey’s theorem for spaces [PDF]
Transactions of the American Mathematical Society, 1979 A short proof is given of the following known result. For all k, r, t there exists n so that if the t-spaces of an n-space are r-colored there exists a k-space all of whose t-spaces are the same color. Here t-space refers initially to a t-dimensional affine space over a fixed finite field. The result is also shown for a more general notion of t-space.
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A Ramsey Theorem for Biased Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2020 A $biased\ graph$ is a pair $(G,\mathcal{B})$, where $G$ is a graph and $\mathcal{B}$ is a collection of `balanced' circuits of $G$ such that no $ $-subgraph of $G$ contains precisely two balanced circuits. We prove a Ramsey-type theorem, showing that if $(G,\mathcal{B})$ is a biased graph which $G$ is a very large complete graph, then $G$ contains a ...
Peter Nelson, Sophia Park
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