Decomposing a graph into bistars

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Bárat and the present author conjectured that, for each tree T, there exists a natural number kT such that the following holds: If G is a kT-edge-connected graph such that |E(T)| divides |E(G)|, then G has a T-decomposition, that is, a decomposition of the edge set into trees each of which is isomorphic to T. The conjecture has been verified for infinitely many paths and for each star. In this paper we verify the conjecture for an infinite family of trees that are neither paths nor stars, namely all the bistars S(k,k+1).

Original languageEnglish
JournalJournal of Combinatorial Theory. Series B
Issue number4
Pages (from-to)504-508
Publication statusPublished - 2013


  • Orientations modulo k
  • Bistar decomposition
  • 3-Flow conjecture


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