{
  "id": "2409.01729",
  "version": "v2",
  "published": "2024-09-03T09:13:12.000Z",
  "updated": "2025-06-21T06:40:52.000Z",
  "title": "On the fractional matching extendability of Cayley graphs of Abelian groups",
  "authors": [
    "Boštjan Kuzman",
    "Primož Šparl"
  ],
  "comment": "21 pages, this is a revised version submitted to the Electronic Journal of Combinatorics",
  "categories": [
    "math.CO"
  ],
  "abstract": "Fractional matching extendability is a concept that brings together two widely studied topics in graph theory, namely that of fractional matchings and that of matching extendability. A {\\em fractional matching} of a graph $\\Gamma$ with edge set $E$ is a function $f$ from $E$ to the real interval $[0,1]$ with the property that for each vertex $v$ of $\\Gamma$, the sum of $f$-values of all the edges incident to $v$ is at most $1$. When this sum equals $1$ for each vertex $v$, the fractional matching is {\\em perfect}. A graph of order at least $2t+1$ is {\\em fractional $t$-extendable} if it contains a matching of size $t$ and if each such matching $M$ can be extended to a fractional perfect matching in the sense that the corresponding function $f$ assigns value $1$ to each edge of $M$. In this paper, we study fractional matching extendability of Cayley graphs of Abelian groups. We show that, except for the odd cycles, all connected Cayley graphs of Abelian groups are fractional $1$-extendable and we classify the fractional $2$-extendable Cayley graphs of Abelian groups. This extends the classification of $2$-extendable (in the classical sense) connected Cayley graphs of Abelian groups of even order from 1995, obtained by Chan, Chen and Yu.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-06-21T06:40:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C70",
      "05C25"
    ],
    "keywords": [
      "abelian groups",
      "connected cayley graphs",
      "study fractional matching extendability",
      "graph theory",
      "edges incident"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}