M. Anholcer

activity

20112025

most citedDistance magic labeling and two products of graphs

20 citations · 99 across the 20 of their papers we have counts for

collaborators

21 papers

math.CO2025

On acyclic b-chromatic number of cubic graphs

Marcin Anholcer, Sylwia Cichacz, Iztok Peterin

Let $G$ be a graph. An acyclic $k$ -coloring of $G$ is a map $c : V (G) \to {1, \dots, k}$ such that $c (u) \neq = c (v)$ for any $uv \in E (G)$ and the subgraph induced by the vertice…

math.CO2025

Global coalition sets in graphs

Nazli Besharati, Doost Ali Mojdeh, Mohammad Reza Samadzadeh +1

Let $G = (V, E)$ be a graph. A subset $S \subseteq V$ is called a global dominating set of $G$ , if it serves as a dominating set in both $G$ and its complement $G$ . We defi…

math.CO2025

Alon-Tarsi for hypergraphs

Marcin Anholcer, Bartłomiej Bosek, Grzegorz Gutowski +6

Given a hypergraph $H = (V, E)$ , define for every edge $e \in E$ a linear expression with arguments corresponding to the vertices. Next, let the polynomial $p_{H}$ be the product of such…

math.CO2022

Majority dominator colorings of graphs

Marcin Anholcer, Azam Sadat Emadi, Doost Ali Mojdeh

Let $G$ be a simple graph of order $n$ . A majority dominator coloring of a graph $G$ is proper coloring in which each vertex of the graph dominates at least half of one color class…

math.CO2022

Mrs. Correct and Majority Colorings

Marcin Anholcer, Bartłomiej Bosek, Jarosław Grytczuk +3

A majority coloring of a directed graph is a vertex coloring in which each vertex has the same color as at most half of its out-neighbors. In this note we simplify some proof techn…

math.CO2022★ 4 cited

On b-acyclic chromatic number of a graph

Marcin Anholcer, Sylwia Cichacz, Iztok Peterin

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)\rightarr…

math.NT2021

On a Problem of Steinhaus

Marcin Anholcer, Bartłomiej Bosek, Jarosław Grytczuk +4

Let $N$ be a positive integer. A sequence $X = (x_{1}, x_{2}, \dots, x_{N})$ of points in the unit interval $[0, 1)$ is piercing if $\{x_1,x_2,\ldots,x_n\}\cap \left[\frac{i}{n},\frac{i+1}{n}…

math.CO2020★ 1 cited

Majority choosability of countable graphs

Marcin Anholcer, Bartłomiej Bosek, Jarosław Grytczuk

In any vertex coloring of a graph some edges have differently colored ends (\emph{good} edges) and some are monochromatic (\emph{bad} edges). In a proper coloring all edges are goo…

math.CO2019

Total vertex product irregularity strength of graphs

Marcin Anholcer, Azam Sadat Emadi, Doost Ali Mojdeh

Consider a simple graph $G$ . We call a labeling $w : E (G) \cup V (G) \to {1, 2, \dots, s}$ (\textit{total vertex}) \textit{product-irregular}, if all product degrees $p d_{G} (v)$ …

math.CO2018

Note on the group edge irregularity strength of graphs

Marcin Anholcer, Sylwia Cichacz

We investigate the \textit{edge group irregularity strength} ( $e s_{g} (G)$ ) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group $G$ of order $s$ , th…

math.CO2018★ 4 cited

Linear bounds on nowhere-zero group irregularity strength and nowhere-zero group sum chromatic number of graphs

Marcin Anholcer, Sylwia Cichacz, Jakub Przybyło

We investigate the \textit{group irregularity strength}, $s_{g} (G)$ , of a graph, i.e. the least integer $k$ such that taking any Abelian group $G$ of order $k$ , there exist…

math.CO2017★ 2 cited

Note on group irregularity strength of disconnected graphs

Marcin Anholcer, Sylwia Cichacz, Rafal Jura +1

We investigate the \textit{group irregularity strength} ( $s_{g} (G)$ ) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group $\gr$ of order $s$ , there exists a f…

math.CO2016

Majority choosability of digraphs

Marcin Anholcer, Bartłomiej Bosek, Jarosław Grytczuk

A \emph{majority coloring} of a digraph is a coloring of its vertices such that for each vertex $v$ , at most half of the out-neighbors of $v$ has the same color as $v$ . A digraph $…

math.OC2015★ 15 cited

Deriving Priorities From Inconsistent PCM using the Network Algorithms

Marcin Anholcer, Janos Fülöp

In several multiobjective decision problems Pairwise Comparison Matrices (PCM) are applied to evaluate the decision variants. The problem that arises very often is the inconsistenc…

math.CO2015★ 14 cited

Spectra of Graphs and Closed Distance Magic Labelings

Marcin Anholcer, Sylwia Cichacz, Iztok Peterin

Let $G = (V, E)$ be a graph of order $n$ . A closed distance magic labeling of $G$ is a bijection $ℓ : V (G) \to {1, \dots, n}$ for which there exists a positive intege…

math.CO2012★ 20 cited

Distance magic labeling and two products of graphs

Marcin Anholcer, Sylwia Cichacz, Iztok Peterin +1

Let $G = (V, E)$ be a graph of order $n$ . A distance magic labeling of $G$ is a bijection $ℓ : V \to 1, ..., n$ for which there exists a positive integer $k$ such that…

math.CO2012

Group Irregular Labelings of Disconnected Graphs

Marcin Anholcer, Sylwia Cichacz

We investigate the \textit{group irregularity strength} ( $s_{g} (G)$ ) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group $\gr$ of order $s$ , there exists a f…

math.CO2012★ 8 cited

Group Sum Chromatic Number of Graphs

Marcin Anholcer, Sylwia Cichacz

We investigate the \textit{group sum chromatic number} ($\gchi(G)$) of graphs, i.e. the smallest value $s$ such that taking any Abelian group $\gr$ of order $s$ , there exists a fun…

math.CO2012★ 17 cited

Group Irregularity Strength of Connected Graphs

Marcin Anholcer, Sylwia Cichacz, Martin Milanic

We investigate the group irregularity strength ( $s_{g} (G)$ ) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group $\gr$ of order $s$ , there exists a function $…

math.CO2011★ 11 cited

Irregular Labellings of Circulant Graphs

Marcin Anholcer

We investigate the \textit{irregularity strength} ( $s (G)$ ) and \textit{total vertex irregularity strength} ( $t v s (G)$ ) of circulant graphs $C i_{n} (1, 2, ..., k)$ and prove that $tvs(Ci_n…

math.CO2011★ 3 cited

Total Vertex Irregularity Strength of Forests

Marcin Anholcer, Michał Karoński, Florian Pfender

We investigate a graph parameter called the total vertex irregularity strength ( $t v s (G)$ ), i.e. the minimal $s$ such that there is a labeling $w: E(G)\cup V(G)\rightarrow \{1,2,..,…