9 papers
A density counterpart of the Scheepers covering property
Leandro Aurichi, Fortunato Maesano, Lyubomyr Zdomskyy
We introduce a density counterpart of the Scheepers covering property and study its relations to known combinatorial density property. In pa…
A topological characterization of end space of infinite graphs via games, subspaces and products
Leandro Aurichi, Gustavo Boska, Davide Giacopello +1
In 1992, Diestel asked which topological spaces could be represented as the end space of some graph. In 2023, Pitz provided a solution to this question by giving a topological char…
Topological remarks on end and edge-end spaces
Leandro Fiorini Aurichi, Paulo Magalhães Júnior, Lucas Real
The notion of ends in an infinite graph might be modified if we consider them as equivalence classes of infinitely edge-connected rays, rather than equivalence classes of infin…
Edge-ends versus topological ends of graphs
Leandro Aurichi, Paulo Magalhães Júnior, Guilherme Eduardo Pinto
Diestel and Kühn proved that the topological ends of an infinite graph are precisely its undominated graph ends, yielding a canonical embedding of the space of topological ends in…
Universal families of rayless graphs
Leandro Fiorini Aurichi, Guilherme Eduardo Pinto
We study the existence and cardinality of universal families for classes of rayless graphs. It is known, by a result of Diestel, Halin, and Vogler, that the class of countable rayl…
On orientations preserving edge-connectivity in infinite graphs
Leandro Aurichi, Paulo Magalhães Júnior, Guilherme Eduardo Pinto
We prove that every 2k-edge-connected graph with countably many edge-ends admits a k-arc-connected orientation, extending the previous result by Assem, Koloschin and Pitz that also…