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, 1/2d < 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.
Original language | English (US) |
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Pages (from-to) | 11-22 |
Number of pages | 12 |
Journal | Annals of Discrete Mathematics |
Volume | 43 |
Issue number | C |
DOIs | |
State | Published - Jan 1 1989 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics