{
  "id": "2003.04804",
  "version": "v1",
  "published": "2020-03-10T15:32:10.000Z",
  "updated": "2020-03-10T15:32:10.000Z",
  "title": "On the balanceability of some graph classes",
  "authors": [
    "Antoine Dailly",
    "Adriana Hansberg",
    "Denae Ventura"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "Given a graph $G$, a 2-coloring of the edges of $K_n$ is said to contain a balanced copy of $G$ if we can find a copy of $G$ such that half of its edges are in each color class. If there exists an integer $k$ such that, for $n$ sufficiently large, every 2-coloring of $K_n$ with more than $k$ edges in each color class contains a balanced copy of $G$, then we say that $G$ is balanceable. Balanceability was introduced by Caro, Hansberg and Montejano, who also gave a structural characterization of balanceable graphs. In this paper, we extend the study of balanceability by finding new sufficient conditions for a graph to be balanceable or not. We use those conditions to fully characterize the balanceability of graph classes such as circulant graphs, rectangular and triangular grids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-10T15:32:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "graph classes",
      "balanceability",
      "balanced copy",
      "color class contains",
      "triangular grids"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}