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  "path": "/abs/2602.22856v1",
  "publishedAt": "2026-02-27T01:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Peter Borg",
    "Yair Caro"
  ],
  "textContent": "**Authors:** Peter Borg, Yair Caro\n\nThe graph isolation problem was introduced by Caro and Hansberg in 2015. It is a vast generalization of the classical graph domination problem and its study is expanding rapidly. In this paper, we address a number of questions that arise naturally. Let $F$ be a graph. We show that the $F$-isolating set problem is NP-complete if $F$ is connected. We investigate how the $F$-isolation number $ι(G,F)$ of a graph $G$ is affected by the minimum degree $d$ of $G$, establishing a bounded range, in terms of $d$ and the orders of $F$ and $G$, for the largest possible value of $ι(G,F)$ with $d$ sufficiently large. We also investigate how close $ι(G,tF)$ is to $ι(G,F)$, using domination and, in suitable cases, the Erdos-Posa property.",
  "title": "Results on three problems on isolation of graphs"
}