{
  "id": "2407.00872",
  "version": "v1",
  "published": "2024-07-01T00:45:09.000Z",
  "updated": "2024-07-01T00:45:09.000Z",
  "title": "Lower Bounds for Multicolor Star-Critical Ramsey Numbers",
  "authors": [
    "Mark Budden",
    "Yash Shamsundar Khobragade",
    "Siddhartha Sarkar"
  ],
  "comment": "18 pages, 6 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The star-critical Ramsey number is a refinement of the concept of a Ramsey number. In this paper, we give equivalent criteria for which the star-critical Ramsey number vanishes. Next, we provide a new general lower bound for multicolor star-critical Ramsey numbers whenever it does not vanish. As an application, we evaluate $r_*(P_k, P_3, P_3)$, where $P_n$ is a path of order $n$. In the process of proving these results, we also show that $r_*(C_5, P_3)=3$, where $C_5$ is a cycle of order $5$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-01T00:45:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C55",
      "05D10"
    ],
    "keywords": [
      "multicolor star-critical ramsey numbers",
      "general lower bound",
      "star-critical ramsey number vanishes",
      "equivalent criteria",
      "refinement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}