{
  "id": "2405.13363",
  "version": "v1",
  "published": "2024-05-22T05:43:56.000Z",
  "updated": "2024-05-22T05:43:56.000Z",
  "title": "Competition-common enemy graphs of degree-bounded digraphs",
  "authors": [
    "Myungho Choi",
    "Hojin Chu",
    "Suh-Ryung Kim"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The competition-common enemy graph (CCE graph) of a digraph $D$ is the graph with the vertex set $V(D)$ and an edge $uv$ if and only if $u$ and $v$ have a common predator and a common prey in $D$. If each vertex of a digraph $D$ has indegree at most $i$ and outdegree at most $j$, then $D$ is called an $\\langle i,j \\rangle$ digraph. In this paper, we fully characterize the CCE graphs of $\\langle 2,2\\rangle$ digraphs. Then we investigate the CCE graphs of acyclic $\\langle 2,2 \\rangle$ digraphs, and prove that any CCE graph of an acyclic $\\langle 2,2 \\rangle$ digraph with at most seven components is interval, and the bound is sharp. While characterizing acyclic $\\langle 2,2 \\rangle$ digraphs that have interval graphs as their competition graphs, Hefner~{\\it et al}. (1991) initiated the study of competition graphs of degree-bounded digraphs. Recently, Lee~{\\em et al}. (2017) and Eoh and Kim (2021) studied phylogeny graphs of degree-bounded digraphs to extend their work.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-22T05:43:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C20",
      "05C75"
    ],
    "keywords": [
      "competition-common enemy graph",
      "degree-bounded digraphs",
      "cce graph",
      "competition graphs",
      "common predator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}