Decomposing a graph into bistars

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Abstract

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
Volume103
Issue number4
Pages (from-to)504-508
ISSN0095-8956
DOIs
Publication statusPublished - 2013

Keywords

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

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