Star arboricity

Noga Alon, Colin McDiarmid, Bruce Reed

Research output: Contribution to journalArticle

34 Scopus citations

Abstract

A star forest is a forest all of whose components are stars. The star arboricity, st(G) of a graph G is the minimum number of star forests whose union covers all the edges of G. The arboricity, A(G), of a graph G is the minimum number of forests whose union covers all the edges of G. Clearly st(G)≥A(G). In fact, Algor and Alon have given examples which show that in some cases st(G) can be as large as A(G)+Ω(logΔ) (where Δ is the maximum degree of a vertex in G). We show that for any graph G, st(G)≤A(G)+O(logΔ).

Original languageEnglish (US)
Pages (from-to)375-380
Number of pages6
JournalCombinatorica
Volume12
Issue number4
DOIs
StatePublished - Dec 1 1992
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

Keywords

  • AMS subject classification code (1991): 05C70, 60C05

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    Alon, N., McDiarmid, C., & Reed, B. (1992). Star arboricity. Combinatorica, 12(4), 375-380. https://doi.org/10.1007/BF01305230