{
  "id": "math/0512120",
  "version": "v1",
  "published": "2005-12-06T08:38:32.000Z",
  "updated": "2005-12-06T08:38:32.000Z",
  "title": "A reconstruction problem related to balance equations-II: the general case",
  "authors": [
    "Bhalchandra D. Thatte"
  ],
  "comment": "Improved version of Discrete Mathematics 194, no. 1-3(1999) 281-284",
  "journal": "Discrete Mathematics 194, no. 1-3(1999) 281-284",
  "categories": [
    "math.CO"
  ],
  "abstract": "A modified $k$-deck of a graph $G$ is obtained by removing $k$ edges of $G$ in all possible ways, and adding $k$ (not necessarily new) edges in all possible ways. Krasikov and Roditty asked if it was possible to construct the usual $k$-edge deck of a graph from its modified $k$-deck. Earlier I solved this problem for the case when $k=1$. In this paper, the problem is completely solved for arbitrary $k$. The proof makes use of the $k$-edge version of Lov\\'asz's result and the eigenvalues of certain matrix related to the Johnson graph. This version differs from the published version. Lemma 2.3 in the published version had a typo in one equation. Also, a long manipulation of some combinatorial expressions was skipped in the original proof of Lemma 2.3, which made it difficult to follow the proof. Here a clearer proof is given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-06T08:38:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C60"
    ],
    "keywords": [
      "reconstruction problem",
      "general case",
      "balance equations-ii",
      "published version",
      "clearer proof"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12120T"
    }
  }
}