The Gilbert-Pollak conjecture, in mathematics, is an unproven statement about the ratio of lengths between Steiner trees and Euclidean minimum spanning trees for the same set of points in the Euclidean plane. It was proposed by Edgar Gilbert and Henry O. Pollak in 1968. It states that for every finite set of points in the plane, the Euclidean minimum spanning tree is no longer than two over the square root of three times the length of the Steiner minimum tree. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
Proposed Year Progress Toward ResolutionA 1990 proof by Du and Hwang turned out to have a serious gap, so the conjecture is not considered proved. 1 Classification
Resolution Status Prize Status
Prize Status (category) Sources
1. Gilbert-Pollak Conjecture (Wikipedia)
Wikimedia FoundationLead section
It was proposed by Edgar Gilbert and Henry O. Pollak in 1968.
Attempted proof
In 1990, Ding-Zhu Du and Frank Kwang-Ming Hwang published a proof that later turned out to have a serious gap.
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