A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Symmetries and Ramsey properties of trees

1999
*
Discrete Mathematics
*

In this paper we show the extent to which a finite

doi:10.1016/s0012-365x(99)90081-x
fatcat:awyk2u4cdfd23ckhcbvzkk5fxi
*tree**of*fixed height is a*Ramsey*object m the class*of**trees**of*the same height can be measured by its*symmetry*group. ... It follows that the complete*trees*are the only*Ramsey*objects in ~. For some further results on the*Ramsey**properties**of**trees*, the reader is referred to [1, 2, 6, 7] . ... Moreover, for a 9iven*tree*T*of*height h,*and*for r >~r(T), there is some T1 E ~-h, such that, for any*tree*T2 E ~-h with [1"2, T1] ~ (~, there is some partition Z : [T2, T] -~ [r] with the*property*...##
###
Page 917 of Mathematical Reviews Vol. , Issue 80C
[page]

1980
*
Mathematical Reviews
*

The derivation

*of*these rules is shown,*and*the relationship between the spectrum*of*G*and*the spectra*of*G,*and*G_ is explained in terms*of*the*symmetry**properties**of*the adjacency matrix*of*G.” 80c:05098 ... It is also surprising that the connected*Ramsey*number r(Tm>K,), where T,, is a*tree*on m vertices, is different for differ- ent types*of**trees*. {For the entire collection see MR 80a:05002a.} ...##
###
Page 2542 of Mathematical Reviews Vol. , Issue 90E
[page]

1990
*
Mathematical Reviews
*

The

*symmetry**of*the spectrum*of*bipartite graphs*and**of*the patterns*of*the powers*of*the adjacency matrix, for example, both extend nicely. ... (i1-MEMP) Extremal theory*and*bipartite graph-*tree**Ramsey*numbers. Proceedings*of*the First Japan Conference on Graph Theory*and*Applications (Hakone, 1986). ...##
###
Page 3160 of Mathematical Reviews Vol. , Issue 90F
[page]

1990
*
Mathematical Reviews
*

The nice

*properties*in (iii)*and*(iv) can be the*property**of*Baire, the*Ramsey**property*, or Lebesgue measurability, quite in- terchangeably. ... The authors show that every A} set*of*reals is*Ramsey*if*and*only if every £} set is*Ramsey*, if*and*only if for each s*and*each r there is a P(D*(r))-generic ultrafilter over L[r}[D*]. ...##
###
Page 6628 of Mathematical Reviews Vol. , Issue 99j
[page]

1999
*
Mathematical Reviews
*

We next discuss the

*Ramsey**properties**of*a large variety*of*structures. We begin with posets*and*then turn to set systems, whereafter we discuss*trees**and*bipartite graphs, respectively. ... From the introduction: “In this paper we discuss the role*of**symmetry*in*Ramsey*theory. A recent survey*of**Ramsey*theory appears in a paper by J. ...##
###
Symmetries between two Ramsey properties
[article]

2001
*
arXiv
*
pre-print

Further we compare two notions

arXiv:math/0109101v1
fatcat:k2bk3a5iynbnhevegwsum7papa
*of*forcing, the Mathias forcing*and*a dual form*of*it,*and*will give some*symmetries*between them. ... In this article we compare the well-known*Ramsey**property*with a dual form*of*it, the so called dual-*Ramsey**property*(which was suggested first by Carlson*and*Simpson). ... Acknowledgements: I would like to thank Pierre Matet for all the fruitful discussions concerning the results in this paper,*and*the referee for valuable comments on an earlier version*of*this paper. ...##
###
Symmetries between two Ramsey properties

1998
*
Archive for Mathematical Logic
*

Further we compare two notions

doi:10.1007/s001530050096
fatcat:zrxmo2enw5a4fdpynb2wdopwwy
*of*forcing, the Mathias forcing*and*a dual form*of*it,*and*will give some*symmetries*between them. ... In this article we compare the well-known*Ramsey**property*with a dual form*of*it, the so called dual-*Ramsey**property*(which was suggested first by Carlson*and*Simpson). ... Acknowledgements: I would like to thank Pierre Matet for all the fruitful discussions concerning the results in this paper,*and*the referee for valuable comments on an earlier version*of*this paper. ...##
###
From abstract alpha-Ramsey theory to abstract ultra-Ramsey theory
[article]

2016
*
arXiv
*
pre-print

We work within the framework

arXiv:1601.03831v1
fatcat:ma6jecv7unaf5m3k7jods4tiim
*of*the Alpha-Theory introduced by Benci*and*Di Nasso. The Alpha-Theory postulates a few natural*properties*for an infinite "ideal" number α. ... The formulation provides an elementary axiomatics for the methods*of*abstract ultra-*Ramsey*theory. The main results are Theorem 10, Theorem 57, Theorem 67*and*Theorem 73. ... By*symmetry*, if either st(T ) ⊑ st(S) ∈ T or st(S) ⊑ st(T ) ∈ S then S ∩ T is an α-*tree*. ...##
###
Rainbow Ramsey simple structures

2016
*
Discrete Mathematics
*

A relational structure R is rainbow

doi:10.1016/j.disc.2016.04.021
fatcat:hckvwt2jeneedjuxv5nq2rgfdy
*Ramsey*if for every finite induced substructure C*of*R*and*every colouring*of*the copies*of*C with countably many colours, such that each colour is used at most k times ... We show that a class*of*homogeneous binary relational structures generalizing the Rado graph are rainbow*Ramsey*. ...*And*similarly for the rainbow*Ramsey**property*. Proof. By*symmetry*it suffices to assume that A is an induced substructure*of*B. Let A δ − → A C k*and*γ : B C → ω be k-delta. ...##
###
Rainbow Ramsey simple structures
[article]

2014
*
arXiv
*
pre-print

A relational structure R is rainbow

arXiv:1411.6678v1
fatcat:2hast4l7uvfgxfglr2qu7qc7f4
*Ramsey*if for every finite induced substructure C*of*R*and*every colouring*of*the copies*of*C with countably many colours, such that each colour is used at most k times ... Via compactness this then implies that for all finite graphs B*and*C*and*k ∈ω, there exists a graph A so that for every colouring*of*the copies*of*C in A such that each colour is used at most k times, ... The second author was supported by NSERC*of*Canada Grant # 690404. The third author was supported by NSERC*of*Canada Grant # 691325. ...##
###
Page 31 of Mathematical Reviews Vol. , Issue 82a
[page]

1982
*
Mathematical Reviews
*

The author shows that if G is a

*tree**and*Y is its set*of*endpoints, then S( Y) is a path all*of*whose points have degree 2 in G. ... If the condition |X | > min X is dropped, we get the usual*Ramsey*relation. It is a remarkable result*of*J. Paris*and*L. ...##
###
The weak Ramsey property and extreme amenability
[article]

2021
*
arXiv
*
pre-print

We extend the Kechris–Pestov–Todorčević correspondence to weak Fraïssé categories

arXiv:2110.01694v1
fatcat:udwgufx4fjfthesthru5plf2rm
*and*automorphism groups*of*generic objects. The new ingredient is the weak*Ramsey**property*. ... We demonstrate the theory on several examples including monoid categories, the category*of*almost linear orders,*and*categories*of*strong embeddings*of**trees*. ... structures*and**Ramsey*-type*properties**of*their finite substructures. ...##
###
Page 3011 of Mathematical Reviews Vol. , Issue 91F
[page]

1991
*
Mathematical Reviews
*

*Properties*

*of*classical

*Ramsey*numbers (in fact the difference

*of*consecutive

*Ramsey*numbers) are used to verify the existence

*of*such families

*of*graphs. ... (SAR-UPAM) On the number

*of*spanning

*trees*

*of*X,,

*and*K,, ,. Discrete Math. 84 (1990), no. 2, 205-207. ...

##
###
Page 54 of Mathematical Reviews Vol. 42, Issue 2
[page]

1971
*
Mathematical Reviews
*

., partitioning

*of*a set*of*objects,*and*S’ is monochromatic. This paper concerns*Ramsey*type theorems relating to edge colourings*of*graphs. ... To prove that P(4)=10, the authors display a 4-regular graph on 10 nodes which has no*symmetry*,*and*the 15 4- regular graphs on 9 nodes, which all have some*symmetry*. R. C. ...##
###
Ramsey equivalence for asymmetric pairs of graphs
[article]

2022
*
arXiv
*
pre-print

The rest

arXiv:2206.03898v1
fatcat:j4cgsutipnctfe4f6l53nlny7u
*of*the paper focuses on pairs*of*the form (T,K_t), where T is a*tree**and*K_t is a complete graph. ... We make progress on the asymmetric version*of*this question*and*identify several non-trivial families*of**Ramsey*equivalent pairs*of*connected graphs. ... We next study*Ramsey*equivalence for pairs*of*the form (T, K t ), where T is a*tree**and*t ≥ 3. ...
« Previous

*Showing results 1 — 15 out of 1,802 results*