On the conjecture of hajós


Hajós conjectured that everys-chromatic graph contains a subdivision ofK s, the complete graph ons vertices. Catlin disproved this conjecture. We prove that almost all graphs are counter-examles in a very strong sense.

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Erdős, P., Fajtlowicz, S. On the conjecture of hajós. Combinatorica 1, 141–143 (1981). https://doi.org/10.1007/BF02579269

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AMS (1980) subject classification

  • 05 C 15
  • 60 C 05