  We prove that the projective dimension of any (hyper)graph can be bounded
from above by the (Castelnuovo-Mumford) regularity of its Levi graph (or
incidence bipartite graph). This in particular brings the use of regularity's
upper bounds on the calculation of projective dimension of (hyper)graphs. When
G is just a (simple) graph, we prove that there exists an induced subgraph H of
G such that prod-dim(G)=reg(S(H)), where S(H) is the subdivision graph of H.
Moreover, we show that known upper bounds on prod-dim(G) involving domination
parameters are in fact upper bounds to reg(S(G)).
