Marcin Stawiski

activity

20182026

most citedA bound for the distinguishing index of regular graphs

12 citations · 12 across the 16 of their papers we have counts for

collaborators

17 papers

math.CO2026

Breaking small automorphisms of graphs of arbitrary cardinality

Marcin Stawiski

We say that an edge colouring $c$ of a graph preserves an automorphism $φ$ if $φ$ maps each edge to an edge of the same colour. Otherwise, we say that $c$ breaks $φ$ . We call an au…

math.CO2026

Irreducible distinguishing colourings and the Axiom of Choice

Marcin Stawiski

We say that a vertex or edge colouring of a graph is distinguishing if the only automorphism that preserves this colouring is the identity. A (proper) distinguishing colouring is i…

math.CO2026

A new problem related to Eulerian graphs

Marcin Stawiski

Let $G$ be a graph, and $H$ be a finite subgraph of $G$ . We say that $H$ is a (semi) $S$ -Eulerian subgraph if there exists a closed (open) trail $T$ in $G$ such that each edge of $…

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.CO2023

List majority edge-colorings of graphs

Rafał Kalinowski, Monika Pilśniak, Marcin Stawiski

A majority edge-coloring of a graph without pendant edges is a coloring of its edges such that, for every vertex $v$ and every color $α$ , there are at most as many edges incident t…

math.CO2023

Breaking small automorphisms by list colourings

Jakub Kwaśny, Marcin Stawiski

For a graph G, we define a small automorphism as one that maps some vertex into its neighbour. We investigate the edge colourings of G that break every small automorphism of G. We…

math.CO2023

List distinguishing index of graphs

Jakub Kwaśny, Marcin Stawiski

We say that an edge colouring breaks an automorphism if some edge is mapped to an edge of a different colour. We say that the colouring is distinguishing if it breaks every non-ide…

math.CO2023

A note on the 1-2-3 Theorem for infinite graphs

Marcin Stawiski

Karoński, Łuczak and Thomason conjectured in 2004 that for every finite graph without isolated edge, the edges can be assigned weights from ${1, 2, 3}$ in such a way that the endve…

math.CO2023

Asymmetrizing infinite trees

Wilfried Imrich, Rafał Kalinowski, Florian Lehner +2

A graph $G$ is asymmetrizable if it has a set of vertices whose setwise stablizer only consists of the identity automorphism. The motion $m$ of a graph is the minimum number of ver…

math.CO2022

The distinguishing index of graphs with infinite minimum degree

Marcin Stawiski, Trevor M. Wilson

The distinguishing index $D^{'} (G)$ of a graph $G$ is the least number of colors necessary to obtain an edge coloring of $G$ that is preserved only by the trivial automorphism. We sho…

math.CO2022

Distinguishing regular graphs from lists

Jakub Kwaśny, Marcin Stawiski

An edge colouring of a graph is called distinguishing if there is no non-trivial automorphism which preserves it. We prove that every at most countable, finite or infinite, connect…

math.CO2021

Factorizations of regular graphs of infinite degree

Marcin Stawiski

Let $H = {H_{i} : i < α}$ be an indexed family of graphs for some ordinal number $α$ . $H$ -decomposition of a graph $G$ is a family $G = {G_{i} : i < α}$ of edge…

math.CO2021

Distinguishing infinite star-free graphs

Marcin Stawiski

Call a colouring of a graph \emph{distinguishing} if the only automorphism of this graph which preserves said colouring is the identity. Let $H$ be an arbitrary graph. We say that…

math.CO2020

The role of the Axiom of Choice in proper and distinguishing colourings

Marcin Stawiski

Call a colouring of a graph distinguishing if the only automorphism which preserves it is the identity. We investigate the role of the Axiom of Choice in the existence of certain p…

math.CO2019

On asymmetric colourings of graphs with bounded degrees and infinite motion

Florian Lehner, Monika Pilśniak, Marcin Stawiski

A vertex colouring of a graph is called asymmetric if the only automorphism which preserves it is the identity. Tucker conjectured that if every automorphism of a connected, locall…

math.CO2019★ 12 cited

A bound for the distinguishing index of regular graphs

Florian Lehner, Monika Pilśniak, Marcin Stawiski

An edge-colouring of a graph is distinguishing, if the only automorphism which preserves the colouring is the identity. It has been conjectured that all but finitely many connected…

math.CO2018

Distinguishing infinite graphs with bounded degrees

Florian Lehner, Monika Pilśniak, Marcin Stawiski

Call a colouring of a graph distinguishing, if the only colour preserving automorphism is the identity. A conjecture of Tucker states that if every automorphism of a graph $G$ move…