{
  "id": "2406.17631",
  "version": "v1",
  "published": "2024-06-25T15:18:21.000Z",
  "updated": "2024-06-25T15:18:21.000Z",
  "title": "Tight Toughness and Isolated Toughness for $\\{K_2,C_n\\}$-factor critical avoidable graph",
  "authors": [
    "Xiaxia Guan",
    "Hongxia Ma",
    "Maoqun Wang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A spannning subgraph $F$ of $G$ is a $\\{K_2,C_n\\}$-factor if each component of $F$ is either $K_{2}$ or $C_{n}$. A graph $G$ is called a $(\\{K_2,C_n\\},n)$-factor critical avoidable graph if $G-X-e$ has a $\\{K_2,C_n\\}$-factor for any $S\\subseteq V(G)$ with $|X|=n$ and $e\\in E(G-X)$. In this paper, we first obtain a sufficient condition with regard to isolated toughness of a graph $G$ such that $G$ is $\\{K_2,C_{n}\\}$-factor critical avoidable. In addition, we give a sufficient condition with regard to tight toughness and isolated toughness of a graph $G$ such that $G$ is $\\{K_2,C_{2i+1}|i \\geqslant 2\\}$-factor critical avoidable respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-25T15:18:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "factor critical avoidable graph",
      "isolated toughness",
      "tight toughness",
      "sufficient condition",
      "spannning subgraph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}