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  "path": "/abs/2603.22204v1",
  "publishedAt": "2026-03-24T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Jacob Fox",
    "Jonathan Tidor"
  ],
  "textContent": "**Authors:** Jacob Fox, Jonathan Tidor\n\nWe prove the existence of optimal separators for intersection graphs of balls and spheres in any dimension $d$. One of our results is that if an intersection graph of $n$ spheres in $\\mathbb{R}^d$ has $m$ edges, then it contains a balanced separator of size $O_d(m^{1/d}n^{1-2/d})$. This bound is best possible in terms of the parameters involved. The same result holds if the balls and spheres are replaced by fat convex bodies and their boundaries.",
  "title": "Separators for intersection graphs of spheres"
}