Paweł Żyliński

activity

20162026

most citedOn domination perfect graphs

8 citations · 12 across the 7 of their papers we have counts for

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7 papers · 1 filter

math.CO2026

Isolation subdivision number of a graph

Magda Dettlaff, Magdalena Lemańska, Merce Mora +2

For a graph $G = (V, E),$ a set $S \subseteq V$ is called an isolating set of $G$ if the set $V - N [S]$ is independent. The minimum cardinality of an isolating set in $G$ is the isolati…

math.CO2026

Isolation critical graphs under multiple edge subdivision

Karl Bartolo, Peter Borg, Magda Dettlaff +2

This paper introduces the notion of an $(ι, q)$ -critical graph. The isolation number of a graph $G$ , denoted by $ι (G)$ and also known as the vertex-edge domination number of $G$ , is…

math.CO2019

Disjoint dominating and 2-dominating sets in graphs

Mateusz Miotk, Jerzy Topp, Paweł Żyliński

A graph $G$ is a $D D_{2}$ -graph if it has a pair $(D, D_{2})$ of disjoint sets of vertices of $G$ such that $D$ is a dominating set and $D_{2}$ is a 2-dominating set of $G$ . We provide…

math.CO2018★ 2 cited

Graphs with equal domination and covering numbers

Andrzej Lingas, Mateusz Miotk, Jerzy Topp +1

A dominating set of a graph $G$ is a set $D \subseteq V_{G}$ such that every vertex in $V_{G} - D$ is adjacent to at least one vertex in $D$ , and the domination number $γ (G)$ of $G$ is th…

math.CO2018★ 8 cited

On domination perfect graphs

Jerzy Topp, Paweł Żyliński

Let $γ (G)$ and $β (G)$ denote the domination number and the covering number of a graph $G$ , respectively. A connected non-trivial graph $G$ is said to be $γ β$ -{perfect} if $γ(H)=β(H…

math.CO2017

Graphs with equal domination and certified domination numbers

Magda Dettlaff, Magdalena Lemańska, Mateusz Miotk +3

A set $D$ of vertices of a graph $G$ is a dominating set of $G$ if every vertex in $V_{G} - D$ is adjacent to at least one vertex in $D$ . The domination number (upper domination number…

math.CO2016

Certified domination

Magda Dettlaff, Magdalena Lemańska, Jerzy Topp +2

Imagine that we are given a set $D$ of officials and a set $W$ of civils. For each civil $x \in W$ , there must be an official $v \in D$ that can serve $x$ , and whenever any such $v…