Paweł Żyliński

activity

20162022

collaborators

6 papers

cs.CG2022

The Rectilinear Steiner Forest Arborescence problem

Łukasz Mielewczyk, Leonidas Palios, Paweł Żyliński

Let $r$ be a point in the first quadrant $Q_{1}$ of the plane $R^{2}$ and let $P \subset Q_{1}$ be a set of points such that for any $p \in P$ , its $x$ - and $y$ -coordinate is at…

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

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

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…