{
  "id": "1508.07627",
  "version": "v1",
  "published": "2015-08-30T19:55:08.000Z",
  "updated": "2015-08-30T19:55:08.000Z",
  "title": "On graphs uniquely defined by their $k$-circular matroids",
  "authors": [
    "José F. De Jesús",
    "Alexander Kelmans"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1508.05364",
  "categories": [
    "math.CO"
  ],
  "abstract": "In 30's Hassler Whitney considered and completely solved the problem $(WP)$ of describing the classes of graphs $G$ having the same cycle matroid $M(G)$. A natural analog $(WP)'$ of Whitney's problem $(WP)$ is to describe the classes of graphs $G$ having the same matroid $M'(G)$, where $M'(G)$ is a matroid on the edge set of $G$ distinct from $M(G)$. For example, the corresponding problem $(WP)' = (WP)_{\\theta }$ for the so-called bicircular matroid $M_{\\theta }(G)$ of graph $G$ was solved by Coulard, Del Greco and Wagner. In our previous paper [arXive:1508.05364] we introduced and studied the so-called $k$-circular matroids $M_k(G)$ for every non-negative integer $k$ that is a natural generalization of the cycle matroid $M(G):= M_0(G)$ and of the bicircular matroid $M_{\\theta }(G):= M_1(G)$ of graph $G$. In this paper (which is a continuation of our previous paper) we establish some properties of graphs guaranteeing that the graphs are uniquely defined by their $k$-circular matroids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-30T19:55:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35",
      "05C99"
    ],
    "keywords": [
      "circular matroids",
      "cycle matroid",
      "bicircular matroid",
      "30s hassler whitney",
      "natural analog"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}