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ramsey_theorem (483B)


      1 # Ramsey theorem
      2 
      3 Consequence: any sufficiently large [undirected_graph] contains either a big [clique] or a big [independent_set]
      4 - so the [union] of both problems is trivial
      5 
      6 Generalizations:
      7 
      8 - more than 2 colors
      9   - https://en.wikipedia.org/wiki/Ramsey%27s_theorem#More_colors
     10 - [hypergraphs]
     11   - https://en.wikipedia.org/wiki/Ramsey%27s_theorem#Hypergraphs
     12 
     13 Can also be useful in [formal_language_theory]: [ramsey_formal_languages]
     14 
     15 Up: [mathematics]
     16 
     17 Aliases: Ramsey's theorem