Since it follows that for large enough the conjecture does not hold by the same token as written in the comment here http://www.openproblemgarden.org/op/total_domination_number_of_a_hypercube
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CSI of Charles University
False
Since
it follows that for large enough 
the conjecture does not hold by the same token as written in the comment here http://www.openproblemgarden.org/op/total_domination_number_of_a_hypercube