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We prove that the projective dimension of any (hyper)graph can be boundedfrom above by the (Castelnuovo-Mumford) regularity of its Levi graph (orincidence bipartite graph). This in particular brings the use of regularity'supper bounds on the calculation of projective dimension of (hyper)graphs. WhenG is just a (simple) graph, we prove that there exists an induced subgraph H ofG 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 dominationparameters are in fact upper bounds to reg(S(G)).

Projective dimension of (hyper)graphs and the Castelnuovo-Mumford regularity of bipartite graphs