The Star Arboricity of Graphs

I. Algor, N. Alon

Research output: Contribution to journalArticle

23 Scopus citations

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 languageEnglish (US)
Pages (from-to)11-22
Number of pages12
JournalAnnals of Discrete Mathematics
Volume43
Issue numberC
DOIs
StatePublished - Jan 1 1989
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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