Karl Bartolo

activity

20232026

collaborators

4 papers

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.CO2025

Solution to a problem on isolation of $3$ -vertex paths

Karl Bartolo, Peter Borg, Dayle Scicluna

The $3$ -path isolation number of a connected $n$ -vertex graph $G$ , denoted by $ι (G, P_{3})$ , is the size of a smallest subset $D$ of the vertex set of $G$ such that the closed neighbo…

math.CO2025

Solution to a $3$ -path isolation problem for subcubic graphs

Karl Bartolo, Peter Borg, Dayle Scicluna

The $3$ -path isolation number of a connected $n$ -vertex graph $G$ , denoted by $ι (G, P_{3})$ , is the size of a smallest subset $D$ of the vertex set of $G$ such that the closed neighbo…

math.CO2023

Isolation of squares in graphs

Karl Bartolo, Peter Borg, Dayle Scicluna

Given a set $F$ of graphs, we call a copy of a graph in $F$ an $F$ -graph. The $F$ -isolation number of a graph $G$ , denoted by $ι(G,\mathcal{…

Isolation critical graphs under multiple edge subdivision

Solution to a problem on isolation of 3-vertex paths

Solution to a 3-path isolation problem for subcubic graphs

Isolation of squares in graphs

Solution to a problem on isolation of $3$ -vertex paths

Solution to a $3$ -path isolation problem for subcubic graphs