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math.CO2024
Remarks on the countable case of the Unfriendly Partition Problem
Leandro Fiorini Aurichi, Lucas Real
The Unfriendly Partition Problem asks whether it is possible to split the vertex set of an infinite graph into two parts so that every vertex has at least as many neighbors in…
math.CO2024★ 2 cited
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…
math.CO2024★ 1 cited
Edge-connectivity between edge-ends of infinite graphs
Leandro Fiorini Aurichi, Lucas Real
In infinite graph theory, the notion of ends, first introduced by Freudenthal and Jung for locally finite graphs, plays an important role when generalizing statements from finite g…