{
  "id": "2006.16072",
  "version": "v1",
  "published": "2020-06-29T14:25:07.000Z",
  "updated": "2020-06-29T14:25:07.000Z",
  "title": "Spatial graph as connected sum of a planar graph and a braid",
  "authors": [
    "Valeriy G. Bardakov",
    "Akio Kawauchi"
  ],
  "comment": "14 pages, 14 figures",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "In this paper we show that every finite spatial graph is a connected sum of a planar graph, which is a forest, i.e. disjoint union of finite number of trees and a tangle. As a consequence we get that any finite spatial graph is a connected sum of a planar graph and a braid. Using these decompositions it is not difficult to find a set of generators and defining relations for the fundamental group of compliment of a spatial graph in 3-space $\\mathbb{R}^3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-29T14:25:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M07",
      "57M25"
    ],
    "keywords": [
      "planar graph",
      "connected sum",
      "finite spatial graph",
      "disjoint union",
      "finite number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}