{
  "id": "2004.06788",
  "version": "v1",
  "published": "2020-04-14T20:07:46.000Z",
  "updated": "2020-04-14T20:07:46.000Z",
  "title": "Reflexive coloring complexes for 3-edge-colorings of cubic graphs",
  "authors": [
    "Fiachra Knox",
    "Bojan Mohar",
    "Nathan Singer"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a 3-colorable graph $X$, the 3-coloring complex $B(X)$ is the graph whose vertices are all the independent sets which occur as color classes in some 3-coloring of $X$. Two color classes $C,D \\in V(B(X))$ are joined by an edge if $C$ and $D$ appear together in a 3-coloring of $X$. The graph $B(X)$ is 3-colorable. Graphs for which $B(B(X))$ is isomorphic to $X$ are termed reflexive graphs. In this paper, we consider 3-edge-colorings of cubic graphs for which we allow half-edges. Then we consider the 3-coloring complexes of their line graphs. The main result of the paper is a surprising outcome that the line graph of any connected cubic triangle-free outerplanar graph is reflexive. We also exhibit some other interesting classes of reflexive line graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-14T20:07:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15"
    ],
    "keywords": [
      "cubic graphs",
      "reflexive coloring complexes",
      "color classes",
      "connected cubic triangle-free outerplanar graph",
      "independent sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}