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The shortest path and the shortest road through n points

Published online by Cambridge University Press:  26 February 2010

L. Few
L. Few
Affiliation:
University College, London.
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Extract

Consider a set of n points lying in a square of side 1. Verblunsky has shown that, if n is sufficiently large, there is some path through all n points whose length does not exceed (2·8n)1/2+2. L. Fejes Tóth has drawn attention to the case when the n points consist of all points of a regular hexagonal lattice lying in the unit square, in which case the length of the shortest path is easily seen to be asymptotically equal to

Type
Research Article
Information
Mathematika , Volume 2 , Issue 2 , December 1955 , pp. 141 - 144
Copyright
Copyright © University College London 1955

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References

page 141 note * Proc. American Math. Sec., 2 (1951), 904–913.CrossRefGoogle Scholar

page 141 note † Math. Zeitschrift, 46 (1940), 83–85.CrossRefGoogle Scholar

page 144 note * Gesammelte Abhandlungen II, 53–100 (§15).