The Friendship Theorem

Karol Pąk

Formalized Mathematics (2012)

  • Volume: 20, Issue: 3, page 235-237
  • ISSN: 1426-2630

Abstract

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In this article we prove the friendship theorem according to the article [1], which states that if a group of people has the property that any pair of persons have exactly one common friend, then there is a universal friend, i.e. a person who is a friend of every other person in the group

How to cite

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Karol Pąk. "The Friendship Theorem." Formalized Mathematics 20.3 (2012): 235-237. <http://eudml.org/doc/267893>.

@article{KarolPąk2012,
abstract = {In this article we prove the friendship theorem according to the article [1], which states that if a group of people has the property that any pair of persons have exactly one common friend, then there is a universal friend, i.e. a person who is a friend of every other person in the group},
author = {Karol Pąk},
journal = {Formalized Mathematics},
keywords = {universal friend},
language = {eng},
number = {3},
pages = {235-237},
title = {The Friendship Theorem},
url = {http://eudml.org/doc/267893},
volume = {20},
year = {2012},
}

TY - JOUR
AU - Karol Pąk
TI - The Friendship Theorem
JO - Formalized Mathematics
PY - 2012
VL - 20
IS - 3
SP - 235
EP - 237
AB - In this article we prove the friendship theorem according to the article [1], which states that if a group of people has the property that any pair of persons have exactly one common friend, then there is a universal friend, i.e. a person who is a friend of every other person in the group
LA - eng
KW - universal friend
UR - http://eudml.org/doc/267893
ER -

References

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  1. [1] Michael Albert. Notes on the friendship theorem, http://www.math.auckland.ac.nz/-~olympiad/training/2006/friendship.pdf. 
  2. [2] Grzegorz Bancerek. Cardinal arithmetics. Formalized Mathematics, 1(3):543-547, 1990. 
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  13. [13] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990. 
  14. [14] Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relative primes. Formalized Mathematics, 1(5):829-832, 1990. 
  15. [15] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990. 
  16. [16] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  17. [17] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 
  18. [18] Edmund Woronowicz and Anna Zalewska. Properties of binary relations. FormalizedMathematics, 1(1):85-89, 1990. 

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