Triangle-Freeness Is Hard To Detect

@article{Jukna2002TriangleFreenessIH,
  title={Triangle-Freeness Is Hard To Detect},
  author={Stasys Jukna and Georg Schnitger},
  journal={Combinatorics, Probability & Computing},
  year={2002},
  volume={11},
  pages={549-569}
}
We show that recognizing the K3-freeness and K4-freeness of graphs is hard, respectively, for two-player nondeterministic communication protocols using exponentially many partitions and for nondeterministic syntactic read-r times branching programs.The key ingredient is a generalization of a colouring lemma, due to Papadimitriou and Sipser, which says that for every balanced redblue colouring of the edges of the complete n-vertex graph there is a set of en2 triangles, none of which is… CONTINUE READING

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