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, 1/2d < st(G) ≤ 1/4d +O(d 2/3(log d)1/3), and that there are d-regular graphs G with st(G) > 1/2d + Ω(log d). 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.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics