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A graph-colouring theorem

Published online by Cambridge University Press:  22 September 2016

R. C. Walker
R. C. Walker*
Affiliation:
29 Station Road, Arlesey, Beds. SG15 6RG
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Extract

Imagine six drawing pins stuck in the wall. If we stretch threads, either red or blue, between every pair of pins, we inevitably create at least one triangle all of one colour. This we shall call Theorem 1: the proof follows.

Consider any pin. From this emanate five threads (since there are five other pins), of which three must be of one colour. We may without loss of generality assume that they are three red threads.

Type
Research Article
Information
The Mathematical Gazette , Volume 60 , Issue 411 , March 1976 , pp. 54 - 57
Copyright
Copyright © Mathematical Association 1976

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References

1. Martin, Gardner, Mathematical games, Scient. Am. 228 (1), 108 (January 1973).Google Scholar