M. Barbieri

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math.GR2025

Separating subsets from their images

Marco Barbieri, MaruÅ¡a LekÅ¡e, PrimoÅ¾ PotoÄnik +1

Let $G$ be a transitive permutation group acting on $I^c ◯$ . In this paper, we introduce and study the parameter $m (G)$ , which denotes the size of the smallest set of points $A$ …

math.GR2025

Every group is the automorphism group of a graph with arbitrarily large genus

Marco Barbieri

We prove that, to every abstract group $G$ , we can associate a sequence of graphs $I^_{n}$ such that the automorphism group of $I^_{n}$ is isomorphic to $G$ and the genus of $I^_{n}$ is…