A counter-example to a lemma about embedding starlike trees into hypercube (Q5948743)

In 1988 \textit{L. Nebeský} [Czech. Math. J. 38(113), No. 4, 705-712 (1988; Zbl 0677.05021)] proved that a star-like tree on \(2^n\) vertices with bipartition into equally large sets spans the \(n\)-cube graph \(Q_n\). The same result was independently proved by \textit{F. Harary} and \textit{M. Lewinter} [Comput. Math. Appl. 15, No. 4, 299-302 (1988; Zbl 0645.05032)]. Unfortunately, the latter proof uses a false lemma---a counterexample is given in this paper.