On the size of maximum renamable Horn sub-CNF

In [Boros, Discrete Appl. Math. 96/97 (1999) 29-40] a lower bound was shown for the size of a maximum renamable Horn sub-CNF of a given CNF. In this short note we show that this bound is tight for complete d-regular formulae on d variables. In fact, we show that this bound is tight even for the size of a maximum q-Horn subformula of a given complete d-regular formulae on d variables; the result for renamable Horn subformulae follows.