Degree Conditions for Spanning Brooms

A broom is a tree obtained by subdividing one edge of the star an arbitrary number of times. In [E. Flandrin, T. Kaiser, R. Kužel, H. Li and Z. Ryjáček, Neighborhood Unions and Extremal Spanning Trees, Discrete Math. 308 (2008), 2343-2350] Flandrin et al. posed the problem of determining degree conditions that ensure a connected graph G contains a spanning tree that is a broom. In this paper, we give one solution to this problem by demonstrating that if G is a connected graph of order n ≥ 56 with δ(G) ≥ n−2 3 , then G contains a spanning broom. This result is best possible.