In any party of 6 people, at least 3 are mutual strangers or at least 3 are acquaintances.
For the friendship theorem of Paul Erdős, Alfréd Rényi, and Vera T. Sós characterizing graphs in which each two vertices have exactly one neighbor, see friendship graph.
78 of the 156 possible friends-strangers graphs with 6 nodes. The other 78 can be obtained by reversing the red and blue colours of each graph. For each graph the red/blue nodes shows a sample triplet of mutual friends/strangers.
The theorem on friends and strangers is a mathematical theorem in an area of mathematics called Ramsey theory.
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mutual strangers (none of them knows either of the other two). See theoremonfriendsandstrangers. This also is a special case of Ramsey's theorem, which...
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theory) Theorem of the cube (algebraic varieties) Theorem of the gnomon (geometry) Theorem of three moments (physics) Theoremonfriendsandstrangers (Ramsey...
create a blue triangle (and each edge of the graph had to be either blue or red). Because of the theoremonfriendsandstrangers, one team or the other...
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Hindman's Theorem confirms the conjecture by Graham and Rothschild and establishes its equivalence with the existence of an ultrafilter on N {\displaystyle...
people living on the same street, or the "tie", for example, to a frequent vendor one would buy from. Such relations with familiar strangers have also been...
couple had five sons and a daughter. Routh was a "kindly man and a good conversationalist with friends, but with strangers he was shy and reserved." Fellow...
was to explain how communication is used to reduce uncertainty between strangers during a first interaction. Uncertainty reduction theory claims that everyone...
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