On restricted colourings ofK n


Given a sample graphH and two integers,n andr, we colourK n byr colours and are interested in the following problem.

Which colourings of the subgraphs isomorphic to H in K n must always occur (and which types of colourings can occur whenK n is coloured in an appropriate way)?

These types of problems include theRamsey theory, where we ask: for whichn andr must a monochromaticH occur. They also include theanti-Ramsey type problems, where we are trying to ensure a totally multicoloured copy ofH, that is, anH each edge of which has different colour.

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Dedicated to Paul Erdős on his seventieth birthday

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Simonovits, M., Sós, V.T. On restricted colourings ofK n . Combinatorica 4, 101–110 (1984). https://doi.org/10.1007/BF02579162

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AMS subject classification (1980)

  • 05 C 35
  • 05 C 55
  • 05 C 38