1 Department of Applied Mathematics and Computer Science, Technical University of Denmark2 Algorithms and Logic, Department of Applied Mathematics and Computer Science, Technical University of Denmark
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).
Journal of Combinatorial Theory. Series B, 2013, Vol 103, Issue 4, p. 504-508