{
  "id": "2002.02285",
  "version": "v1",
  "published": "2019-12-22T03:11:03.000Z",
  "updated": "2019-12-22T03:11:03.000Z",
  "title": "On Alphatrion's Conjecture about Hamiltonian paths in hypercubes",
  "authors": [
    "Steppan Konoplev"
  ],
  "comment": "Alphatrion is an alias and the real name of the person behind this conjecture is not known",
  "categories": [
    "math.CO"
  ],
  "abstract": "Alphatrion conjectured that it is possible to label the vertices of an $n$-dimensional hypercube with distinct positive integers such that for every Hamiltonian path $a_1, \\dots, a_{2^n},$ we have $a_i + a_{i+1}$ prime for all $i.$ We prove the conjecture by proving the more general result that a graph $G = (V, E)$ can be labeled with distinct positive integers such that the edge sum for all $e \\in E$ is prime if and only if $G$ is bipartite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-22T03:11:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamiltonian path",
      "alphatrions conjecture",
      "distinct positive integers",
      "dimensional hypercube",
      "general result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}