The structure of minimal Steiner trees in the neighborhoods of the lunes of their edges
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We give a complete description of small neighborhoods of the closures of lunes of the edges of Steiner minimal trees (Theorem 1.1); to this end, we prove a generalization of a stabilization theorem for embedded locally minimal trees ; the case of two such disjoint trees is considered (Theorem 2.2).
KeywordsSteiner minimal tree locally minimal tree lune of an edge of a tree linear graph shortest tree
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- 2.A. O. Ivanov and A. A. Tuzhilin, The Theory of Extremal Nets (Izd. IKI, Moscow, 2003)] [in Russian].Google Scholar