Extending partial isometries of antipodal graphs

Abstract

We prove EPPA (extension property for partial automorphisms) for all antipodal classes from Cherlin's list of metrically homogeneous graphs, thereby answering a question of Aranda et al. This paper should be seen as the first application of a new general method for proving EPPA which can bypass the lack of an automorphism-preserving completion. It is done by combining the recent strengthening of the Herwig--Lascar theorem by Hubička, Nešetřil and the author with the ideas of the proof of EPPA for two-graphs by Evans et al.

Accepted to Discrete Mathematics

References in corpus (7)

• All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms)
• Ramsey expansions of metrically homogeneous graphs
• A combinatorial proof of the extension property for partial isometries
• Amalgamation and Symmetry: From Local to Global Consistency in The Finite
• Combinatorial Properties of Metrically Homogeneous Graphs
• Semigroup-valued metric spaces
• Forbidden cycles in metrically homogeneous graphs

Cited by in corpus (8)

• Ramsey expansions of metrically homogeneous graphs
• EPPA for two-graphs and antipodal metric spaces
• Simplicity of the automorphism groups of generalised metric spaces
• Semigroup-valued metric spaces
• Extending partial automorphisms of $n$-partite tournaments
• Structural Ramsey Theory and the Extension Property for Partial Automorphisms
• Extension property for partial automorphisms of the $n$-partite and semigeneric tournaments
• Twenty years of Nešetřil's classification programme of Ramsey classes