  A consequence of the surgery theorem of Gromov and Lawson is that every
closed, simply-connected 6-manifold admits a Riemannian metric of positive
scalar curvature. For metrics of positive Ricci curvature it is widely open
whether a similar result holds; there are no obstructions known for those
manifolds to admit a metric of positive Ricci curvature, while the number of
examples known is limited. In this article we introduce a new description of
certain $6k$-dimensional manifolds via labeled bipartite graphs and use an
earlier result of the author to construct metrics of positive Ricci curvature
on these manifolds. In this way we obtain many new examples, both spin and
non-spin, of $6k$-dimensional manifolds with a metric of positive Ricci
curvature.
