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Abstract
A certain relationship between a recent conjecture by F.Y. Wu (1979) and one by W. Klein et al. (1978) is established through considering a three-colour site percolation problem, where the three sublattices of a triangular lattice are populated with probability s1, s2 and s3, respectively. Both conjectures imply the same critical condition for various special cases of this three-colour model, including the threshold probability 1/ square root 2 for the honeycomb site problem. Existing numerical estimates provide strong evidence against this threshold value, hence against both conjectures.
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