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On Pattern Ramsey Numbers of Graphs
2004
Graphs and Combinatorics
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The pattern Ramsey numbers of such families are called constrained Ramsey numbers in [7] . ...
The smallest such N is the (pattern) Ramsey number R(F ) of F . ...
doi:10.1007/s00373-004-0562-y
fatcat:kwozlhqgrffe5l5cvaralz6you
Ramsey Numbers of Interval 2-chromatic Ordered Graphs
[article]
2018
arXiv
pre-print
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We obtain lower bounds linear in the number of vertices for the Ramsey numbers of certain classes of 2-ichromatic ordered graphs. ...
An ordered graph G is a graph together with a specified linear ordering on the vertices, and its interval chromatic number is the minimum number of independent sets consisting of consecutive vertices that ...
Thus we obtain lower bounds on Ramsey numbers for these ordered graphs. ...
arXiv:1805.05900v1
fatcat:jg7sornqovb6raqbo7dyrigjsq
Constrained Ramsey numbers of graphs
2002
Journal of Graph Theory
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The pattern Ramsey numbers of such families are called constrained Ramsey numbers in [7] . ...
The smallest such N is the (pattern) Ramsey number R(F ) of F . ...
doi:10.1002/jgt.10072
fatcat:iuikbucfjbavxfkn52ehvkd46e
Recurrence of Space-Time Events
2015
Journal of Modern Physics
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In this Ramsey theorem inspired model, the regular and repeated patterns are interpreted as identical or semi-identical space-time causal chains. ...
We use Ramsey theorem to prove that there's always a possibility of predictability no matter how chaotic the system is. ...
Applying Ramsey theorem on a countably infinite or suffeciently large number of space-time events emphasizes the existence of regular patterns in the causal structure of space-time events. ...
doi:10.4236/jmp.2015.613182
fatcat:6xccoiox7zgethp3cyp5if6tca
The complexity of proving that a graph is Ramsey
[article]
2013
arXiv
pre-print
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We show a superpolynomial lower bound on the length of resolution proofs that G is c-Ramsey, for every graph G. ...
Our proof makes use of the fact that every Ramsey graph must contain a large subgraph with some of the statistical properties of the random graph. ...
Lower bounds for Ramsey graphs We prove Theorem 3, that for any c-Ramsey graph G on n vertices, L(Ψ G ) ≥ n Ω(log n) . ...
arXiv:1303.3166v1
fatcat:f3sffmoqozhthagv4cplmoijxe
Rainbow Generalizations of Ramsey Theory: A Survey
2010
Graphs and Combinatorics
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In this work, we collect Ramsey-type results concerning rainbow and proper edge colorings of graphs. Editions ...
Definition 4 The pattern Ramsey number for a Ramsey family F of patterns is the smallest integer n 0 such that in every coloring of K n with n ≥ n 0 , there exists some pattern in F . ...
Pattern Ramsey Theory A color pattern is defined to be a graph with colored edges. ...
doi:10.1007/s00373-010-0891-3
fatcat:ytvtt2g4hnhglbyx725xof43de
Page 2762 of Mathematical Reviews Vol. , Issue 98E
[page]
1998
Mathematical Reviews
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The authors used computer algorithms to construct cyclic graphs on a prime number of vertices, and thus derived explicit lower bounds for some classical two-color Ramsey numbers. ...
Summary: “The harmonious chromatic number of a graph G, ...
Research problems
2003
Discrete Mathematics
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Steiner extension of undirected graphs A Steiner extension of a ÿnite undirected graph G is a Steiner triple system S such that the points of S are the vertices of G and such that each triple in S contains ...
Other comments and information about partial or full solutions should be sent to Professor West (for possible later updates on the status of published problems). PROBLEM 412. ...
In general, zero-sum Ramsey numbers are not monotone. The state of the art for zero-sum Ramsey numbers is described in [6, 7] . ...
doi:10.1016/s0012-365x(03)00207-3
fatcat:x43ekuospjc6xjrkzcsd5r4fcm
Page 3208 of Mathematical Reviews Vol. , Issue 2003e
[page]
2003
Mathematical Reviews
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Ramsey numbers based on cubic residues. ...
Detailed results are presented for 16 cases of p, for which numerical lower bounds on the corre- sponding two-color classical Ramsey numbers are given, namely p+1< R(cl(G)+1,in(G) +1). ...
Rainbow generalizations of Ramsey theory - a dynamic survey
2014
Theory and Applications of Graphs
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In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs. ...
The authors of [68] also found the Gallai Ramsey numbers for all trees of order at most 6. Regarding paths in general, the following represents the best known bounds. ...
Acknowledgement The authors would like to thank Maria Axenovich, Tao Jiang and the referee for helpful comments and corrections on the initial publication of this work. ...
doi:10.20429/tag.2014.000101
fatcat:zawfrrlt4jc4fbtiebsbpprsli
Off-diagonal ordered Ramsey numbers of matchings
[article]
2018
arXiv
pre-print
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For ordered graphs G and H, the ordered Ramsey number r_<(G,H) is the smallest n such that every red/blue edge coloring of the complete graph on vertices {1,... ...
One number of interest, first studied by Conlon, Fox, Lee, and Sudakov, is the "off-diagonal" ordered Ramsey number r_<(M, K_3), where M is an ordered matching on n vertices. ...
I would like to thank Asaf Ferber for suggesting that I study ordered Ramsey numbers. I'd also like to thank Ankur Moitra and Davesh Maulik for their advice and support. ...
arXiv:1808.04025v1
fatcat:skxzmlf2drfmfef5xzh5mov33y
Symmetry and the Ramsey Degrees of Finite Relational Structures
1999
Journal of combinatorial theory. Series A
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The number, t(A), if it exists, is called the Ramsey degree of A. Thus A is a Ramsey object iff t(A)=1. ...
We show for classes of finite relational structures, including graphs, binary posets, and bipartite graphs, how this measure depends on the symmetries of the structure. 1999 Academic Press In this paper ...
We shall determine the Ramsey degrees of bipartite graphs, binary posets and so-called :-patterns [1] . ...
doi:10.1006/jcta.1998.2910
fatcat:e75ff3gsbzfsfdte7wqfhvj4ha
Off-Diagonal Ordered Ramsey Numbers of Matchings
2019
Electronic Journal of Combinatorics
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For ordered graphs $G$ and $H$, the ordered Ramsey number $r_<(G,H)$ is the smallest $n$ such that every red/blue edge coloring of the complete ordered graph on vertices $\{1,\dots,n\}$ contains either ...
One number of interest, first studied by Conlon, Fox, Lee, and Sudakov, is the off-diagonal ordered Ramsey number $r_<(M, K_3)$, where $M$ is an ordered matching on $n$ vertices. ...
I would like to thank Asaf Ferber for suggesting that I study ordered Ramsey numbers. I'd also like to thank Ankur Moitra and Davesh Maulik for their advice and support. ...
doi:10.37236/8085
fatcat:asg6bijfwraifh4f7megaxcsym
The complexity of proving that a graph is Ramsey
2016
Combinatorica
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We show a superpolynomial lower bound on the length of resolution proofs that G is c-Ramsey, for every graph G. ...
Our proof makes use of the fact that every c-Ramsey graph must contain a large subgraph with some properties typical for random graphs. ...
Introduction The proof of the existence of c-Ramsey graphs, that is, graphs that have no clique or independent set of size c log n, was one of the first applications of the probabilistic method in combinatorics ...
doi:10.1007/s00493-015-3193-9
fatcat:xtmpehkseba7bh3xup3z6cua2e
The Complexity of Proving That a Graph Is Ramsey
[chapter]
2013
Lecture Notes in Computer Science
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We show a superpolynomial lower bound on the length of resolution proofs that G is c-Ramsey, for every graph G. ...
Our proof makes use of the fact that every c-Ramsey graph must contain a large subgraph with some properties typical for random graphs. ...
Introduction The proof of the existence of c-Ramsey graphs, that is, graphs that have no clique or independent set of size c log n, was one of the first applications of the probabilistic method in combinatorics ...
doi:10.1007/978-3-642-39206-1_58
fatcat:jpfhq2676fhsvb2li5wi2o662q
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