Geodesic
Ramsey precompact expansions of homogeneous directed graphs
Jakub Jasiński1 ; Claude Laflamme1 ; Lionel Nguyen Van Thé2 ; Robert Woodrow1
1University of Calgary
2Université d'Aix-Marseille
The electronic journal of combinatorics, Tome 21 (2014) no. 4
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In 2005, Kechris, Pestov and Todorčević provided a powerful tool to compute an invariant of topological groups known as the universal minimal flow, immediately leading to an explicit representation of this invariant in many concrete cases. 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. In this paper, we show that the age of any homogeneous directed graph allows a Ramsey precompact expansion. Moreover, we verify the relative expansion properties and consequently describe the respective universal minimal flows.
DOI : 10.37236/3840
Classification : 05C55, 05D10, 05C20, 37B05
Mots-clés : Ramsey theory, homogeneous directed graphs, precompact expansions

Jakub Jasiński  1   ; Claude Laflamme  1   ; Lionel Nguyen Van Thé  2   ; Robert Woodrow  1

1 University of Calgary
2 Université d'Aix-Marseille 
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     title = {Ramsey precompact expansions of homogeneous directed graphs},
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     year = {2014},
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     number = {4},
     doi = {10.37236/3840},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/3840/}
}
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Jakub Jasiński; Claude Laflamme; Lionel Nguyen Van Thé; Robert Woodrow. Ramsey precompact expansions of homogeneous directed graphs. The electronic journal of combinatorics, Tome 21 (2014) no. 4. doi: 10.37236/3840

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