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pro vyhledávání: '"Rekvényi, Kamilla"'
Autor:
Barbieri, Marco, Rekvényi, Kamilla
We give a simplified version of the proofs that, outside of their isolated vertices, the complement of the enhanced power graph and of the power graph are connected of diameter at most $3$.
Comment: 3 pages
Comment: 3 pages
Externí odkaz:
http://arxiv.org/abs/2411.05429
A base for a finite permutation group $G \le \mathrm{Sym}(\Omega)$ is a subset of $\Omega$ with trivial pointwise stabiliser in $G$, and the base size of $G$ is the smallest size of a base for $G$. Motivated by the interest in groups of base size two
Externí odkaz:
http://arxiv.org/abs/2410.22613
Autor:
Rekvényi, Kamilla
The orbital diameter of a primitive permutation group is the maximal diameter of its orbital graphs. There has been a lot of interest in bounds for the orbital diameter. In this paper we provide explicit bounds on the diameters of groups of primitive
Externí odkaz:
http://arxiv.org/abs/2409.15960
Autor:
Lee, Melissa, Rekvényi, Kamilla
The intersection graph $\Delta_G$ of a finite group $G$ is a simple graph with vertices the non-trivial proper subgroups of $G$, and an edge between two vertices if their corresponding subgroups intersect non-trivially. These graphs were introduced b
Externí odkaz:
http://arxiv.org/abs/2403.04157
Publikováno v:
Comm. Algebra, 52(9):3750--3761, 2024
Let $G$ be a finite non-abelian simple group, $C$ a non-identity conjugacy class of $G$, and $\Gamma_C$ the Cayley graph of $G$ based on $C \cup C^{-1}$. Our main result shows that in any such graph, there is an involution at bounded distance from th
Externí odkaz:
http://arxiv.org/abs/2402.08497
Autor:
Rekvényi, Kamilla
The orbital diameter of a primitive permutation group is the maximal diameter of its orbital graphs. There has been a lot of interest in bounds for the orbital diameter. In this paper we provide explicit bounds on the diameters of groups of simple di
Externí odkaz:
http://arxiv.org/abs/2102.09867
Autor:
Rekvényi, Kamilla
Publikováno v:
In Journal of Combinatorial Theory, Series A August 2022 190
The main contribution of this paper is a formula for the number of acyclic orientations of a complete bipartite, $K_{n_1,n_2},$ revealing that it is equal to the poly-Bernoulli number $B_{n_1}^{(-n_2)}$ introduced in 1997 by Kaneko. We also give a si
Externí odkaz:
http://arxiv.org/abs/1412.3685