{
  "id": "2106.03414",
  "version": "v1",
  "published": "2021-06-07T08:30:28.000Z",
  "updated": "2021-06-07T08:30:28.000Z",
  "title": "Intertwining connectivities for vertex-minors and pivot-minors",
  "authors": [
    "Duksang Lee",
    "Sang-il Oum"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that for pairs $(Q,R)$ and $(S,T)$ of disjoint subsets of vertices of a graph $G$, if $G$ is sufficiently large, then there exists a vertex $v$ in $V(G)-(Q\\cup R\\cup S\\cup T)$ such that there are two ways to reduce $G$ by a vertex-minor operation while preserving the connectivity between $Q$ and $R$ and the connectivity between $S$ and $T$. Our theorem implies an analogous theorem of Chen and Whittle (2014) for matroids restricted to binary matroids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-07T08:30:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C40",
      "05C50",
      "05C83",
      "G.2.2"
    ],
    "keywords": [
      "intertwining connectivities",
      "connectivity",
      "pivot-minors",
      "theorem implies",
      "disjoint subsets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}