{
  "id": "2104.13505",
  "version": "v1",
  "published": "2021-04-27T23:23:33.000Z",
  "updated": "2021-04-27T23:23:33.000Z",
  "title": "Clique number of Xor products of Kneser graphs",
  "authors": [
    "András Imolay",
    "Anett Kocsis",
    "Ádám Schweitzer"
  ],
  "comment": "18 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this article we investigate a problem in graph theory, which has an equivalent reformulation in extremal set theory similar to the problems researched in \"A general 2-part Erd\\H{o}s-Ko-Rado theorem\" by Gyula O.H. Katona, who proposed our problem as well. In the graph theoretic form we examine the clique number of the Xor product of two isomorphic $KG(N,k)$ Kneser graphs. Denote this number with $f(k,N)$. We give lower and upper bounds on $f(k,N)$, and we solve the problem up to a constant deviation depending only on $k$, and find the exact value for $f(2,N)$ if $N$ is large enough. We also compute that $f(k,k^2)$ is asymptotically equivalent to $k^2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-27T23:23:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D05",
      "05C69",
      "05C76"
    ],
    "keywords": [
      "kneser graphs",
      "xor product",
      "clique number",
      "extremal set theory similar",
      "graph theoretic form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}