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pro vyhledávání: '"CICHACZ, SYLWIA"'
Autor:
Cichacz, Sylwia
We provide a summary of research on disjoint zero-sum subsets in finite Abelian groups, which is a branch of additive group theory and combinatorial number theory. An orthomorphism of a group $\Gamma$ is defined as a bijection $\varphi$ $\Gamma$ such
Externí odkaz:
http://arxiv.org/abs/2410.22245
Autor:
Cichacz, Sylwia
If $A$ is a finite Abelian group, then a labeling $f \colon E (G) \rightarrow A$ of the edges of some graph $G$ induces a vertex labeling on $G$; the vertex $u$ receives the label $\sum_{v\in N(u)}f (v)$, where $N(u)$ is an open neighborhood of the v
Externí odkaz:
http://arxiv.org/abs/2409.09136
Autor:
Cichacz, Sylwia
A complete mapping of a group $\Gamma$ is a bijection $\varphi\colon \Gamma\to \Gamma$ for which the mapping $x \mapsto x+\varphi(x)$ is a bijection. In this paper we consider the existence of a complete mapping $\varphi$ of $\Gamma$ and a partition
Externí odkaz:
http://arxiv.org/abs/2408.07411
Autor:
Cichacz, Sylwia, Dzúrik, Martin
In this paper we would like to introduce some new methods for studying magic type-colorings of graphs or domination of graphs, based on combinatorial spectrum on polynomial rings. We hope that this concept will be potentially useful for the graph the
Externí odkaz:
http://arxiv.org/abs/2401.01680
We study the problem of finding a minimum $k$-critical-bipartite graph of order $(n,m)$: a bipartite graph $G=(U,V;E)$, with $|U|=n$, $|V|=m$, and $n>m>1$, which is $k$-critical-bipartite, and the tuple $(|E|, \Delta_U, \Delta_V)$, where $\Delta_U$ a
Externí odkaz:
http://arxiv.org/abs/2307.07315
Autor:
Cichacz, Sylwia, Krupińska, Barbara
We investigate the \textit{group irregular strength} $(s_g(G))$ of graphs, i.e the smallest value of $s$ such that for any Abelian group $\Gamma$ of order $s$ exists a function $g\colon E(G) \rightarrow \Gamma$ such that sums of edge labels at every
Externí odkaz:
http://arxiv.org/abs/2306.11914
Autor:
Cichacz, Sylwia
Let $\overrightarrow{G}$ be a directed graph of order $n$ with no component of order less than $4$, and let $\Gamma$ be a finite Abelian group such that $|\Gamma|\geq n+6$. We show that there exists a mapping $\psi$ from the arc set $E(\overrightarro
Externí odkaz:
http://arxiv.org/abs/2303.08712
Publikováno v:
Discussiones Mathematicae Graph Theory 44(4) (2024) 1471-1484
Vertex-fault-tolerance was introduced by Hayes~\cite{Hayes1976} in 1976, and since then it has been systematically studied in different aspects. In this paper we study $k$-vertex-fault-tolerant graphs for $p$ disjoint complete graphs of order $c$, i.
Externí odkaz:
http://arxiv.org/abs/2212.06892
Publikováno v:
Comp. Appl. Math. 42, 21 (2023)
Let $G$ be a graph. We introduce the acyclic b-chromatic number of $G$ as an analogue to the b-chromatic number of $G$. An acyclic coloring of a graph $G$ is a map $c:V(G)\rightarrow \{1,\dots,k\}$ such that $c(u)\neq c(v)$ for any $uv\in E(G)$ and t
Externí odkaz:
http://arxiv.org/abs/2206.06478
Autor:
Cichacz, Sylwia, Suchan, Karol
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 26:3, Combinatorics (October 25, 2024) dmtcs:12361
The following problem has been known since the 80s. Let $\Gamma$ be an Abelian group of order $m$ (denoted $|\Gamma|=m$), and let $t$ and $\{m_i\}_{i=1}^{t}$, be positive integers such that $\sum_{i=1}^t m_i=m-1$. Determine when $\Gamma^*=\Gamma\setm
Externí odkaz:
http://arxiv.org/abs/2203.09395