Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-24T15:57:16.588Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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).