Extending partial isometries of antipodal graphs

Konečný, Matěj

doi:10.1016/j.disc.2019.111633

Cited by 3 publications

(1 citation statement)

References 32 publications

(74 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The class of all finite integer-valued antipodal metric spaces of diameter 3 has coherent EPPA. This theorem also holds for all other antipodal metric spaces from Cherlin's catalogue of metrically homogeneous graphs [Che17], see [Kon19b]. It answers affirmatively a question of Aranda, Bradley-Williams, Hubička, Karamanlis, Kompatscher, Konečný and Pawliuk [ABWH + 17] and completes the analysis of EPPA for all classes from Cherlin's catalogue.…”

Section: Introductionmentioning

confidence: 59%

EPPA for two-graphs and antipodal metric spaces

Evans

Hubička

Konečný³

et al. 2020

Proc. Amer. Math. Soc.

Self Cite

View full text Add to dashboard Cite

We prove that the class of finite two-graphs has the extension property for partial automorphisms (EPPA, or Hrushovski property), thereby answering a question of Macpherson. In other words, we show that the class of graphs has the extension property for switching automorphisms. 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.The class of two-graphs is an important new example which behaves differently from all the other known classes with EPPA: Two-graphs do not have the amalgamation property with automorphisms (APA), their 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.

show abstract

Section: Introductionmentioning

confidence: 59%

EPPA for two-graphs and antipodal metric spaces

Evans

Hubička

Konečný³

et al. 2020

Proc. Amer. Math. Soc.

Self Cite

View full text Add to dashboard Cite

show abstract

Simplicity of the automorphism groups of generalised metric spaces

et al. 2021

View full text Add to dashboard Cite

All those EPPA classes (strengthenings of the Herwig–Lascar theorem)

Hubička

Konečný²,

Nešetřil

2022

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

Let A \mathbf {A} be a finite structure. We say that a finite structure B \mathbf {B} is an extension property for partial automorphisms (EPPA)-witness for A \mathbf {A} if it contains A \mathbf {A} as a substructure and every isomorphism of substructures of A \mathbf {A} extends to an automorphism of B \mathbf {B} . Class C \mathcal C of finite structures has the EPPA (also called the Hrushovski property) if it contains an EPPA-witness for every structure in C \mathcal C . We develop a systematic framework for combinatorial constructions of EPPA-witnesses satisfying additional local properties and thus for proving EPPA for a given class C \mathcal C . Our constructions are elementary, self-contained and lead to a common strengthening of the Herwig–Lascar theorem on EPPA for relational classes defined by forbidden homomorphisms, the Hodkinson–Otto theorem on EPPA for relational free amalgamation classes, its strengthening for unary functions by Evans, Hubička and Nešetřil and their coherent variants by Siniora and Solecki. We also prove an EPPA analogue of the main results of J. Hubička and J. Nešetřil: All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms), thereby establishing a common framework for proving EPPA and the Ramsey property. There are numerous applications of our results, we include a solution of a problem related to a class constructed by the Hrushovski predimension construction. We also characterize free amalgamation classes of finite Γ L \Gamma \!_L -structures with relations and unary functions which have EPPA.

show abstract

Extending partial isometries of antipodal graphs

Cited by 3 publications

References 32 publications

EPPA for two-graphs and antipodal metric spaces

EPPA for two-graphs and antipodal metric spaces

Simplicity of the automorphism groups of generalised metric spaces

All those EPPA classes (strengthenings of the Herwig–Lascar theorem)

Contact Info

Product

Resources

About