  In a recent paper, Duval, Goeckner, Klivans and Martin disproved the
longstanding conjecture by Stanley, that every Cohen-Macaulay simplicial
complex is partitionable. We construct counterexamples to this conjecture that
are even \emph{balanced}, i.e., their underlying graph has a minimal coloring.
This answers a question by Duval et al. in the negative.
