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On Pattern Ramsey Numbers of Graphs

Robert E. Jamison, Douglas B. West
2004 Graphs and Combinatorics  
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]

Dana Neidinger, Douglas B. West
2018 arXiv   pre-print
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

Robert E. Jamison, Tao Jiang, Alan C. H. Ling
2002 Journal of Graph Theory  
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

Nasr Ahmed
2015 Journal of Modern Physics  
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]

Massimo Lauria, Pavel Pudlák, Vojtěch Rödl, Neil Thapen
2013 arXiv   pre-print
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

Shinya Fujita, Colton Magnant, Kenta Ozeki
2010 Graphs and Combinatorics  
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  
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  
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  
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

Shinya Fujita, Colton Magnant, Kenta Ozeki
2014 Theory and Applications of Graphs  
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]

Dhruv Rohatgi
2018 arXiv   pre-print
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

Willem L. Fouché
1999 Journal of combinatorial theory. Series A  
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

Dhruv Rohatgi
2019 Electronic Journal of Combinatorics  
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

Massimo Lauria, Pavel Pudlák, Vojtěch Rödl, Neil Thapen
2016 Combinatorica  
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]

Massimo Lauria, Pavel Pudlák, Vojtěch Rödl, Neil Thapen
2013 Lecture Notes in Computer Science  
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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