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On Pattern Ramsey Numbers of Graphs

2004
*
Graphs and Combinatorics
*

The

doi:10.1007/s00373-004-0562-y
fatcat:kwozlhqgrffe5l5cvaralz6you
*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 . ...##
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Ramsey Numbers of Interval 2-chromatic Ordered Graphs
[article]

2018
*
arXiv
*
pre-print

We obtain lower bounds linear in the

arXiv:1805.05900v1
fatcat:jg7sornqovb6raqbo7dyrigjsq
*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*. ...##
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Constrained Ramsey numbers of graphs

2002
*
Journal of Graph Theory
*

The

doi:10.1002/jgt.10072
fatcat:iuikbucfjbavxfkn52ehvkd46e
*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 . ...##
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Recurrence of Space-Time Events

2015
*
Journal of Modern Physics
*

In this

doi:10.4236/jmp.2015.613182
fatcat:6xccoiox7zgethp3cyp5if6tca
*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. ...##
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The complexity of proving that a graph is Ramsey
[article]

2013
*
arXiv
*
pre-print

We show a superpolynomial lower bound

arXiv:1303.3166v1
fatcat:f3sffmoqozhthagv4cplmoijxe
*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) . ...##
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Rainbow Generalizations of Ramsey Theory: A Survey

2010
*
Graphs and Combinatorics
*

In this work, we collect

doi:10.1007/s00373-010-0891-3
fatcat:ytvtt2g4hnhglbyx725xof43de
*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. ...##
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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, ...##
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Research problems

2003
*
Discrete Mathematics
*

Steiner extension

doi:10.1016/s0012-365x(03)00207-3
fatcat:x43ekuospjc6xjrkzcsd5r4fcm
*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] . ...##
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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). ...

##
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Rainbow generalizations of Ramsey theory - a dynamic survey

2014
*
Theory and Applications of Graphs
*

In this work, we collect

doi:10.20429/tag.2014.000101
fatcat:zawfrrlt4jc4fbtiebsbpprsli
*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. ...##
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Off-diagonal ordered Ramsey numbers of matchings
[article]

2018
*
arXiv
*
pre-print

For ordered

arXiv:1808.04025v1
fatcat:skxzmlf2drfmfef5xzh5mov33y
*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. ...##
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Symmetry and the Ramsey Degrees of Finite Relational Structures

1999
*
Journal of combinatorial theory. Series A
*

The

doi:10.1006/jcta.1998.2910
fatcat:e75ff3gsbzfsfdte7wqfhvj4ha
*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] . ...##
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Off-Diagonal Ordered Ramsey Numbers of Matchings

2019
*
Electronic Journal of Combinatorics
*

For ordered

doi:10.37236/8085
fatcat:asg6bijfwraifh4f7megaxcsym
*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. ...##
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The complexity of proving that a graph is Ramsey

2016
*
Combinatorica
*

We show a superpolynomial lower bound

doi:10.1007/s00493-015-3193-9
fatcat:xtmpehkseba7bh3xup3z6cua2e
*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 ...##
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The Complexity of Proving That a Graph Is Ramsey
[chapter]

2013
*
Lecture Notes in Computer Science
*

We show a superpolynomial lower bound

doi:10.1007/978-3-642-39206-1_58
fatcat:jpfhq2676fhsvb2li5wi2o662q
*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 ...
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