Peter Borg

collaborators

4 papers

math.CO2025

Solution to a problem on isolation of cliques in uniform hypergraphs

Peter Borg

A copy of a hypergraph $F$ is called an $F$ -copy. Let $K_{k}^{r}$ denote the complete $r$ -uniform hypergraph whose vertex set is $[k] = {1, \dots, k}$ (that is, the edges of $K_{k}^{r}$ …

math.CO2025

Isolation of non-triangle cycles in graphs

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…

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

Proof of a conjecture on isolation of graphs with a universal vertex

Peter Borg, Alastair Farrugia

A copy of a graph $F$ is called an $F$ -copy. For any graph $G$ , the $F$ -isolation number of $G$ , denoted by $ι (G, F)$ , is the size of a smallest subset $D$ of the vertex set of $G$ …

Solution to a problem on isolation of cliques in uniform hypergraphs

Isolation of non-triangle cycles in graphs

Solution to a problem on isolation of 3-vertex paths

Proof of a conjecture on isolation of graphs with a universal vertex

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