Star arboricity

Abstract

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

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

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AMS subject classification code (1991)

  • 05 C 70
  • 60 C 05