{
  "annotation_id": "7f92d264-33cb-45ab-9488-6a23312f2183",
  "date_created": "2026-02-17T05:53:12.328000Z",
  "date_modified": "2026-02-17T05:53:12.328000Z",
  "file_hash": "d2a60b39070c6b36ddeaee0495acd8f598e1ae6426516e13bd94fe0e1c5e8be3",
  "private": false,
  "record": {
    "abstract": "Let $k\\ge 2$ be a positive integer and let $G$ be a simple graph of order $n$ with minimum degree $\\delta$. A graph $G$ is said to have property $P(k, d)$ if it contains $k$ edge-disjoint spanning trees and an additional forest $F$ with edge number $|E(F)| \u003e \\frac{d-1}{d}(n-1)$, such that if $F$ is not a spanning tree, then $F$ has a component with at least $d$ edges. Let $D(G)$ be the distance matrix of $G$. We denote $\\rho_D(G)$ as the largest eigenvalue of $D(G)$, which is called the distance spectral radius of $G$. In this paper, we investigate the relationship between the distance spectral radius and the property $P(k, \\delta)$. We prove that for a connected graph $G$ of order $n \\ge 2k+8$ with minimum degree $\\delta \\ge k+2$, if $\\rho_D(G) \\le \\rho_D(K_{k-1} \\vee (K_{n-k} \\cup K_1))$, then $G$ possesses property $P(k, \\delta)$. Furthermore, for a connected balanced bipartite graph $G$ of order $n \\ge 4k+8$ with minimum degree $\\delta \\ge k+2$, we show that if $\\rho_D(G) \\le \\rho_D(K_{\\frac{n}{2}, \\frac{n}{2}} \\setminus E(K_{1, \\frac{n}{2}-k+1}))$, then $G$ also possesses property $P(k, \\delta)$. Our results generalize the work of Fan et al. [Discrete Appl. Math. 376 (2025), 31--40] from the existence of $k$ edge-disjoint spanning trees to the more refined structural property $P(k, \\delta)$.",
    "arxiv_id": "2601.07895",
    "authors": [
      "Yongbin Gao",
      "Ligong Wang"
    ],
    "categories": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Distance spectral radius conditions for edge-disjoint spanning trees and a forest with constraints",
    "url": "https://arxiv.org/abs/2601.07895",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bb573c34-c2b0-4a57-85df-6beedc066d74",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}