Covering regular graphs with forests of small trees

H. Assiyatun, N. C. Wormald

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A (d, k) -forest is a forest consisting of trees whose diameters are at most d and whose maximum vertex degree,Δ is at most k. The (d, k)-arboricity of a graph G is the minimum number of (d, k)-forests needed to cover E(G). This concept is a common generalization of linear k-arboricity and star arboricity. Using a probabilistic approach developed recently for linear karboricity, we obtain an upper bound on the (d, k)-arboricity of r-regular graphs.

Original languageEnglish
Pages (from-to)219-226
Number of pages8
JournalAustralasian Journal of Combinatorics
Publication statusPublished - 2000
Externally publishedYes

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