{
  "annotation_id": "0fb6e2a2-2dbd-42b8-b93e-0f9c3b3c0305",
  "date_created": "2026-02-17T05:53:11.948000Z",
  "date_modified": "2026-02-17T05:53:11.948000Z",
  "file_hash": "cf6a6ff73ec3950e87a601ca4e6a386b9caca5d461200718d964f573fce959b4",
  "private": false,
  "record": {
    "abstract": "The topic of this paper is related to the well-known notion of unit distance graphs. Take a graph with its edges coloured red and blue such that for some $d$ it can be mapped into the plane with all vertices going to distinct points, the red edges to segments of length $1$ and the blue edges to segments of length $d$. We define the range of this graph to be the set of such numbers $d$. It is easy to show that the range of any edge-bicoloured graph consists of finitely many intervals with algebraic endpoints, and we now prove that any such set with a finite positive upper and lower bound is the range of a suitable graph.",
    "arxiv_id": "2601.07828",
    "authors": [
      "P\u00e9ter \u00c1goston"
    ],
    "categories": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "On the range of two-distance graphs",
    "url": "https://arxiv.org/abs/2601.07828",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "26f6af65-59de-4090-a949-75c3f42dc4fc",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}