R. Kalinowski

activity

20222026

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Showing math.COShow all

6 papers · 1 filter

math.CO2026

Strong majority colorings of graphs

Rafał Kalinowski, Mateusz Kamyczura, Monika Pilśniak +1

Motivated by majority vertex-colorings of graphs and digraphs and majority edge-colorings of graphs, we introduce two concepts of strong majority colorings. A strong majority verte…

math.CO2025

Quasi-majority neighbor sum distinguishing edge-colorings

Rafał Kalinowski, Monika Pilśniak, Elżbieta Sidorowicz +1

In this paper, a $k$ -edge-coloring of $G$ is any mapping $c : E (G) ⟶ [k]$ . The edge-coloring $c$ of $G$ naturally defines a vertex-coloring $σ_{c} : V (G) \to N$ ,…

math.CO2025

Distinguishing finite and infinite trees of arbitrary cardinality

Wilfried Imrich, Rafał Kalinowski, Florian Lehner +2

Let $G$ be a finite or infinite graph and $m (G)$ the minimum number of vertices moved by the non-identity automorphisms of $G$ . We are interested in bounds on the supremum $Δ (G)$ o…

math.CO2025

Distinguishing symmetric digraphs by proper arc-colourings of type I

Rafał Kalinowski, Monika Pilśniak, Magdalena Prorok

A symmetric digraph $G$ is obtained from a simple graph $G$ by replacing each edge $uv$ with a pair of opposite arcs $uv$ , $v u$ . An arc-…

math.CO2025

On the distinguishing chromatic number in hereditary graph classes

Christoph Brause, Rafał Kalinowski, Monika Pilśniak +1

The distinguishing chromatic number of a graph $G$ , denoted $χ_{D} (G)$ , is the minimum number of colours in a proper vertex colouring of $G$ that is preserved by the identity automor…

math.CO2022

Majority Edge-Colorings of Graphs

Felix Bock, Rafał Kalinowski, Johannes Pardey +3

We propose the notion of a majority $k$ -edge-coloring of a graph $G$ , which is an edge-coloring of $G$ with $k$ colors such that, for every vertex $u$ of $G$ , at most half the edge…