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- W2088497613 abstract "The long-standing conjecture of Gilbert and Pollak states that for any set of n given points in the Euclidean plane, the ratio of the length of a Steiner minimal tree and the length of a minimal (spanning) tree is at least 32. This conjecture was shown to be true for n = 3 by Gilbert and Pollak, and for n = 4 by Pollak. Recently, Du, Yao and Hwang used a different approach to give a shorter proof for n = 4. In this paper we continue this approach to prove the conjecture for n = 5. Such results for small n are useful in obtaining bounds for the ratio of the two lengths in the general case." @default.
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- W2088497613 date "1985-03-01" @default.
- W2088497613 modified "2023-09-30" @default.
- W2088497613 title "The steiner ratio conjecture is true for five points" @default.
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- W2088497613 doi "https://doi.org/10.1016/0097-3165(85)90073-1" @default.
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