{
  "id": "1909.06354",
  "version": "v1",
  "published": "2019-09-13T17:57:05.000Z",
  "updated": "2019-09-13T17:57:05.000Z",
  "title": "New lower bounds on the size-Ramsey number of a path",
  "authors": [
    "Deepak Bal",
    "Louis DeBiasio"
  ],
  "comment": "15 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that for all graphs with at most $(3.75-o(1))n$ edges there exists a 2-coloring of the edges such that every monochromatic path has order less than $n$. This was previously known to be true for graphs with at most $2.5n-7.5$ edges. We also improve on the best-known bounds in the $r$-color case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-13T17:57:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "size-ramsey number",
      "lower bounds",
      "color case",
      "monochromatic path"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}