Note on packing of edge-disjoint spanning trees in sparse random graphs

• DOI: 10.48550/arxiv.1301.1097
• Publication Date: 2013-01-01
• Authors: Xiaolin Chen; Xueliang Li; Huishu Lian
• Keywords: Disjoint sets; Degree (music)

The \emph{spanning tree packing number} of a graph $G$ is the maximum number edge-disjoint spanning trees contained in $G$. Let $k\geq 1$ be fixed integer. Palmer and Spencer proved that almost every random process, hitting time for having $k$ equals minimum degree $k$. In this paper, we prove any $p$ such $(\log n+ω(1))/n\leq p\leq (1.1\log n)/n$, surely $G(n,p)$ satisfies equal to degree. Note bound will allow function $n$, sense improve result Spencer. Moreover, also obtain $p\geq (51\log less than