Spanning subdivisions in Dirac graphs

Abstract

AbstractWe show that for every $n\in \mathbb N$ and $\log n\le d\lt n$ , if a graph $G$ has $N=\Theta (dn)$ vertices and minimum degree $(1+o(1))\frac{N}{2}$ , then it contains a spanning subdivision of every $n$ -vertex $d$ -regular graph.