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The Steiner ratio conjecture for six points. (English) Zbl 0739.05034

Summary: We prove the Steiner ratio conjecture for six points. We use the variational approach discussed in detail in our forthcoming paper “A variational approach to the Steiner network problem”, Ann. Oper. Res. In Section 1 we give a brief discussion of the variational technique and pose the Steiner ratio conjecture as a problem of variations. In Section 2 we give some useful general variations and discuss decomposition. In Section 3 we give a proof of the Steiner conjecture for six points.

MSC:

05C05 Trees
94C15 Applications of graph theory to circuits and networks
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