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Ramsey expansions of metrically homogeneous graphs [article]

Andrés Aranda, David Bradley-Williams, Jan Hubička, Miltiadis Karamanlis, Michael Kompatscher, Matěj Konečný, Micheal Pawliuk
2017 arXiv   pre-print
We show that, with the exception of tree-like graphs, all metric spaces in the catalogue have precompact Ramsey expansions (or lifts) with the expansion property.  ...  We discuss the Ramsey property, the existence of a stationary independence relation and the coherent extension property for partial isometries (coherent EPPA) for all classes of metrically homogeneous  ...  The third author would like to thank to Gregory Cherlin for discussions concerning finite set of obstacles of metrically homogeneous graphs.  ... 
arXiv:1707.02612v2 fatcat:b5qkd5fhijdxnoiwlus4zlkztm

Structural Ramsey Theory and the Extension Property for Partial Automorphisms [article]

Jan Hubička
2020 arXiv   pre-print
We survey recent developments concerning two properties of classes of finite structures: the Ramsey property and the extension property for partial automorphisms (EPPA).  ...  Acknowledgement The author is grateful to David Evans, Gregory Cherlin and Matěj Konečný for number of remarks and suggestions which improved presentation of this paper.  ...  Results on metrically homogeneous graphs are all based on a close study of completion algorithms for partial structures.  ... 
arXiv:2010.05041v1 fatcat:sracoxd7gzbkxhelalepybixgi

Combinatorial Properties of Metrically Homogeneous Graphs [article]

Matěj Konečný
2018 arXiv   pre-print
This thesis is a contribution to the programme; we find Ramsey expansions of the primitive 3-constrained classes from Cherlin's catalogue of metrically homogeneous graphs.  ...  In 2005, Nešetřil initiated a systematic study of the so-called Ramsey classes of finite structures.  ...  This result is then used in Chapter 6 to find Ramsey expansions and prove the so-called EPPA of metrically homogeneous graphs.  ... 
arXiv:1805.07425v1 fatcat:jia72p5m3vc6hflolgkkeqylvi

Semigroup-valued metric spaces [article]

Matěj Konečný
2019 arXiv   pre-print
results on Λ-ultrametric spaces and the results of Aranda et al. on Cherlin's primitive 3-constrained metrically homogeneous graphs.  ...  Sauer's S-metric spaces, Conant's generalised metric spaces, Braunfeld's Λ-ultrametric spaces or Cherlin's metrically homogeneous graphs).  ...  . , δ}, ⊕) is indeed a commutative semigroup for every valid choice of δ, C and M . Acknowledgements.  ... 
arXiv:1810.08963v2 fatcat:5pta7k7sabfo3feytw7mop5pye

A Survey On Structural Ramsey Theory And Topological Dynamics With The Kechris-Pestov-Todorcevic Correspondence In Mind

Lionel Nguyen Van Thé
2015 Zenodo  
As an immediate consequence, it triggered a new interest for structural Ramsey theory. The purpose of the present paper is to present a self-contained survey of the corresponding developments.  ...  SANU, Belgrade ; International audience ; In 2005, Kechris, Pestov and Todorcevic established a surprising correspondence between structural Ramsey theory and topological dynamics.  ...  However, for most classes of metric spaces, the search for Ramsey expansions is largely open. Vector spaces.  ... 
doi:10.5281/zenodo.1471599 fatcat:hlaz3o7lkzf6dh3sjgxqvfhp7a

A survey on structural Ramsey theory and topological dynamics with the Kechris-Pestov-Todorcevic correspondence in mind [article]

Lionel Nguyen Van Thé
2014 arXiv   pre-print
As an immediate consequence, it triggered a new interest for structural Ramsey theory. The purpose of the present paper is to present a self-contained survey of the corresponding developments.  ...  In 2005, Kechris, Pestov and Todorcevic established a surprising correspondence between structural Ramsey theory and topological dynamics.  ...  However, for most classes of metric spaces, the search for Ramsey expansions is largely open. 5.5. Vector spaces.  ... 
arXiv:1412.3254v2 fatcat:nlaso4d63zdipiltn4hqbii77i

Structural Ramsey Theory With The Kechris-Pestov-Todorcevic Correspondence In Mind

Lionel Nguyen Van Thé
2013 Zenodo  
My work elaborates on the former and concentrates on two themes: structural Ramsey theory and topological dynamics of Polish transformation groups.  ...  This area has recently known a considerable expansion thanks to two major contributions by Kechris, Pestov and Todorcevic, and by Kechris and Rosendal.  ...  simply called homogeneity.  ... 
doi:10.5281/zenodo.1471603 fatcat:jeptngaxanfzpa5lvglyzk3ifq

EPPA for two-graphs and antipodal metric spaces [article]

David Evans, Jan Hubička, Matěj Konečný, Jaroslav Nešetřil
2019 arXiv   pre-print
Ramsey expansion has to add a graph, it is not known if they have coherent EPPA and even EPPA itself cannot be proved using the Herwig--Lascar theorem.  ...  We present a short, self-contained, purely combinatorial proof which also proves EPPA for the class of integer valued antipodal metric spaces of diameter 3, answering a question of Aranda et al.  ...  By a similar argument, one can prove that the "best" Ramsey expansion (that is, with the expansion property) of these structures is still the ordered random graph.  ... 
arXiv:1812.11157v2 fatcat:cznhri67hzb75jcsgf5keuf7gy

Ramsey precompact expansions of homogeneous directed graphs [article]

Jakub Jasiński, Claude Laflamme, Lionel Nguyen Van Thé, Robert Woodrow
2014 arXiv   pre-print
In this paper, we show that the age of any homogeneous directed graph allows a Ramsey precompact expansion.  ...  More recently, the framework was generalized allowing for further applications, and the purpose of this paper is to apply these new methods in the context of homogeneous directed graphs.  ...  For example, we have examples of homogeneous metric spaces whose Ramsey precompact expansions are still unknown.  ... 
arXiv:1310.6466v3 fatcat:qcdnv6bdpbcszpvje4ve3som6y

Ramsey theory of homogeneous structures: current trends and open problems [article]

Natasha Dobrinen
2021 arXiv   pre-print
Cognate areas, including infinite dimensional Ramsey theory of homogeneous structures and partition theory of uncountable structures, are also discussed.  ...  This article highlights historical achievements in the partition theory of countable homogeneous relational structures, and presents recent work, current trends, and open problems.  ...  She thanks Jan Hubička, Dragan Mašulović, Matěj Konečný, Lionel Nguyen Van Thé, and Andy Zucker for valuable feedback on drafts of this paper.  ... 
arXiv:2110.00655v1 fatcat:yl4tfcwtrng5vlalcpbukys5xe

Forbidden cycles in metrically homogeneous graphs [article]

Jan Hubička, Michael Kompatscher, Matěj Konečný
2018 arXiv   pre-print
This analysis is a key to showing that the ages of metrically homogeneous graphs have Ramsey expansions and the extension property for partial automorphisms.  ...  This has further applications, for example, interpreting the graphs as semigroup-valued metric spaces or homogenizations of ω-categorical {1,δ}-edge-labelled graphs.  ...  Thus it was not clear which examples of homogeneous structures do not have a good Ramsey expansion.  ... 
arXiv:1808.05177v1 fatcat:axjmnjrntzabvj4w2h67u62y2q

Completing graphs to metric spaces [article]

Andrés Aranda, David Bradley-Williams, Eng Keat Hng, Jan Hubička, Miltiadis Karamanlis, Michael Kompatscher, Matěj Konečný, Micheal Pawliuk
2019 arXiv   pre-print
We prove that certain classes of metrically homogeneous graphs omitting triangles of odd short perimeter as well as triangles of long perimeter have the extension property for partial automorphisms and  ...  we describe their Ramsey expansions.  ...  do) or the Ramsey property when applied to slight modifications of the generalised algorithm in nearly all other classes of metrically homogeneous graphs with finite diameter in Cherlin's catalogue, as  ... 
arXiv:1706.00295v3 fatcat:sfxputmtkve5xeg26qtkf5jwl4

Homogeneity and related topics: An extended bibliography [article]

Gregory Cherlin
2021 arXiv   pre-print
We give a bibliography of works relating to homogeneous structures in the sense of Fra\"iss\'e, and related topics, mainly through 2016, with some narrow updating through 2021.  ...  graphs Cherlin [2022] ; finite or locally finite metrically homogeneous graphs: Cameron [1980] , Hedman and Pong [2010] , Macpherson [1982] (using Dunwoody [1982] ), cf.  ...  Thomas [1993] ; real measurement: Alper [1985] , [1987] ; (3) Canonical expansions: Thomas [1994] (4) 1-homogeneity in the sense of Myers: Gardiner and McAvaney [1983] , McAvaney [2002] , Myers  ... 
arXiv:2111.15429v2 fatcat:di6lzukkvzdwlcvabb7lozrdha

Infinite Limits of Finite-Dimensional Permutation Structures, and their Automorphism Groups: Between Model Theory and Combinatorics [article]

Samuel Braunfeld
2018 arXiv   pre-print
As a first approximation to this problem, we prove the undecidability of the corresponding decision problem in the category of graphs.  ...  which requires proving a structural Ramsey theorem for all the associated amalgamation classes.  ...  Homogeneous Finite-Dimensional Permutation Structures as Ramsey Expansions of Λ-Ultrametric Spaces 8.  ... 
arXiv:1805.04219v1 fatcat:w3vpswxpu5gx7htiuead545yg4

Ramsey expansions of Λ-ultrametric spaces [article]

Samuel Braunfeld
2017 arXiv   pre-print
When Λ is finite and distributive, there exists a generic Λ-ultrametric space, and we here identify a family of Ramsey expansions for that space.  ...  This then allows a description the universal minimal flow of its automorphism group, and also implies the Ramsey property for all known homogeneous finite-dimensional permutation structures, i.e. structures  ...  Let F be a homogeneous structure, and F * a precompact relational expansion of F .  ... 
arXiv:1710.01193v1 fatcat:noj3aujjzrccnohpmadqi2izjm
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