Andrés Aranda
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Andrés Aranda has a total of 19 co-authors. Here are the top co-authors by number of shared publications:
- David Hartman
Computer Science Institute of Charles University, Faculty of Mathematics and Physics, Charles University, Prague 1, Czech Republic
3 shared publications - Dániel Tamás Soukup
Institute of Mathematics University of Vienna Kolingasse 14-16 1090 Wien, Austria
3 shared publications - Jan Hubička
Department of Applied Mathematics (KAM), Charles University, Prague, Czech Republic
3 shared publications - Michael Kompatscher
Department of Algebra, Charles University, Sokolovská 83, 18675 Praha 8, Czechia
3 shared publications - Miltiadis Karamanlis
Department of Mathematics National and Kapodistrian University of Athens Greece
3 shared publications - Claude Laflamme
Department University of Calgary
2 shared publications
Latest Publications
- Open Access
Ramsey expansions of metrically homogeneous graphs
We investigate Ramsey expansions, the coherent extension property for partial isometries (EPPA), and the existence of a stationary independence relation for all classes of metrically homogeneous graphs from Cherlin's catalogue. 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. With two exceptions we can also characterise the existence of a stationary independence relation and coherent EPPA. Our results are a contribution to Ne\v{s}et\v{r}il's classification programme of Ramsey classes and can be seen as empirical evidence of the recent convergence in techniques employed to establish the Ramsey property, the expansion property, EPPA and the existence of a stationary independence relation. At the heart of our proof is a canonical way of completing edge-labelled graphs to metric spaces in Cherlin's classes. The existence of such a ``completion algorithm'' then allows us to apply several strong results in the areas that imply EPPA or the Ramsey property. The main results have numerous consequences for the automorphism groups of the Fraisse limits of the classes. As corollaries, we prove amenability, unique ergodicity, existence of universal minimal flows, ample generics, small index property, 21-Bergman property and Serre's property (FA).
Open AccessRamsey expansions of metrically homogeneous graphs
We investigate Ramsey expansions, the coherent extension property for partial isometries (EPPA), and the existence of a stationary independence relation for all classes of metrically homogeneous graphs from Cherlin's catalogue. 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. With two exceptions we can also characterise the existence of a stationary independence relation and coherent EPPA. Our results are a contribution to Ne\v{s}et\v{r}il's classification programme of Ramsey classes and can be seen as empirical evidence of the recent convergence in techniques employed to establish the Ramsey property, the expansion property, EPPA and the existence of a stationary independence relation. At the heart of our proof is a canonical way of completing edge-labelled graphs to metric spaces in Cherlin's classes. The existence of such a ``completion algorithm'' then allows us to apply several strong results in the areas that imply EPPA or the Ramsey property. The main results have numerous consequences for the automorphism groups of the Fraisse limits of the classes. As corollaries, we prove amenability, unique ergodicity, existence of universal minimal flows, ample generics, small index property, 21-Bergman property and Serre's property (FA).
- Open Access
IB-homogeneous graphs
The Lachlan-Woodrow Theorem identifies ultrahomogeneous graphs up to isomorphism. Recently, the present author and D. Hartman classified MB-homogeneous graphs up to bimorphism-equivalence. We extend those results in this paper, showing that every IB-homogeneous graph is either ultrahomogeneous or MB-homogeneous, and thus all the IB-homogeneous graphs are known up to bimorphism-equivalence.
Open AccessIB-homogeneous graphs
The Lachlan-Woodrow Theorem identifies ultrahomogeneous graphs up to isomorphism. Recently, the present author and D. Hartman classified MB-homogeneous graphs up to bimorphism-equivalence. We extend those results in this paper, showing that every IB-homogeneous graph is either ultrahomogeneous or MB-homogeneous, and thus all the IB-homogeneous graphs are known up to bimorphism-equivalence.
- 30 September 2020
- Published by Elsevier in Discrete Mathematics
- Vol. 344 (1) , 112153
A universal partition result for infinite homogeneous -free and related graphs- 30 September 2020
- Published by Elsevier in Discrete Mathematics
- Vol. 344 (1) , 112153
A universal partition result for infinite homogeneous -free and related graphs- 1 March 2020
- Published by Elsevier in European Journal of Combinatorics
- Vol. 85
The independence number of HH-homogeneous graphs and a classification of MB-homogeneous graphs
- 1 March 2020
- Published by Elsevier in European Journal of Combinatorics
- Vol. 85
The independence number of HH-homogeneous graphs and a classification of MB-homogeneous graphs
- Open Access
The poset of morphism-extension classes of countable graphs
Let $\mathrm{XY_{L,T}}$ denote the class of countably infinite $L$-structures that satisfy the axioms $T$ and in which all homomorphisms of type X (these could be homomorphisms, monomorphisms, or isomorphisms) between finite substructures of $M$ are restrictions of an endomorphism of $M$ of type Y (for example, an automorphism or a surjective endomorphism). Lockett and Truss introduced 18 such morphism-extension classes for relational structures. For a given pair $L,T$, however, two or more morphism-extension properties may define the same class of structures. In this paper, we establish all equalities and inequalities between morphism-extension classes of countable (undirected, loopless) graphs.Open AccessThe poset of morphism-extension classes of countable graphs
Let $\mathrm{XY_{L,T}}$ denote the class of countably infinite $L$-structures that satisfy the axioms $T$ and in which all homomorphisms of type X (these could be homomorphisms, monomorphisms, or isomorphisms) between finite substructures of $M$ are restrictions of an endomorphism of $M$ of type Y (for example, an automorphism or a surjective endomorphism). Lockett and Truss introduced 18 such morphism-extension classes for relational structures. For a given pair $L,T$, however, two or more morphism-extension properties may define the same class of structures. In this paper, we establish all equalities and inequalities between morphism-extension classes of countable (undirected, loopless) graphs. - Open Access
The independence number of HH-homogeneous graphs and a classification of MB-homogeneous graphs
We show that the independence number of a countably infinite HH-homogeneous graph that does not contain the Rado graph as a spanning subgraph is finite and present a classification of MB-homogeneous graphs up to bimorphism-equivalence as a consequence.
Open AccessThe independence number of HH-homogeneous graphs and a classification of MB-homogeneous graphs
We show that the independence number of a countably infinite HH-homogeneous graph that does not contain the Rado graph as a spanning subgraph is finite and present a classification of MB-homogeneous graphs up to bimorphism-equivalence as a consequence.
- 1 July 2019
- Published by Elsevier in Journal of Combinatorial Theory, Series B
- Vol. 137, 1-9
Balanced independent sets in graphs omitting large cliques
- 1 July 2019
- Published by Elsevier in Journal of Combinatorial Theory, Series B
- Vol. 137, 1-9
Balanced independent sets in graphs omitting large cliques
- Open Access
Completing graphs to metric spaces
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.
Open AccessCompleting graphs to metric spaces
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.
- Open Access
Morphism extension classes of countable $L$-colored graphs
In~\cite{Hartman:2014}, Hartman, Hubi\v cka and Ma\v sulovi\'c studied the hierarchy of morphism extension classes for finite $L$-colored graphs, that is, undirected graphs without loops where sets of colors selected from $L$ are assigned to vertices and edges. They proved that when $L$ is a linear order, the classes $MH_L$ and $HH_L$ coincide, and the same is true for vertex-uniform finite $L$-colored graphs when $L$ is a diamond. In this paper, we explore the same question for countably infinite $L$-colored graphs. We prove that $MH_L=HH_L$ if and only if $L$ is a linear order.Open AccessMorphism extension classes of countable $L$-colored graphs
In~\cite{Hartman:2014}, Hartman, Hubi\v cka and Ma\v sulovi\'c studied the hierarchy of morphism extension classes for finite $L$-colored graphs, that is, undirected graphs without loops where sets of colors selected from $L$ are assigned to vertices and edges. They proved that when $L$ is a linear order, the classes $MH_L$ and $HH_L$ coincide, and the same is true for vertex-uniform finite $L$-colored graphs when $L$ is a diamond. In this paper, we explore the same question for countably infinite $L$-colored graphs. We prove that $MH_L=HH_L$ if and only if $L$ is a linear order.