  We study the ground-state (gs) phase diagram of the frustrated spin-1/2
$J_{1}$-$J_{2}$-$J_{3}$ antiferromagnet with $J_{2} = J_{3} =\kappa J_1$ on the
honeycomb lattice, using coupled-cluster theory and exact diagonalization
methods. We present results for the gs energy, magnetic order parameter,
spin-spin correlation function, and plaquette valence-bond crystal (PVBC)
susceptibility. We find a N\'eel antiferromagnetic (AFM) phase for $\kappa <
\kappa_{c_{1}} \approx 0.47$, a collinear striped AFM phase for $\kappa >
\kappa_{c_{2}} \approx 0.60$, and a paramagnetic PVBC phase for $\kappa_{c_{1}}
\lesssim \kappa \lesssim \kappa_{c_{2}}$. The transition at $\kappa_{c_{2}}$
appears to be of first-order type, while that at $\kappa_{c_{1}}$ is
continuous. Since the N\'eel and PVBC phases break different symmetries our
results favor the deconfinement scenario for the transition at
$\kappa_{c_{1}}$.
