The star arboricity of graphs

Abstract A star forest is a forest whose connected components are stars. The star arboricity st(G) of a graph G is the minimum number of star forests whose union covers all edges of G. We show that for every d-regular graph G, 1 2 d 1 2 d + O(d 2 3 (logd) 1 3 , and that there are d-regular graphs G with st(G)> 1 2 d + omega;(logd). We also observe that the star arboricity of any planar graph is at most 6 and that there are planar graphs whose star arboricity is at least 5.