  Using large scale Monte Carlo simulations on a uniformly frustrated 3DXY
model, we report a first order vortex lattice melting transition in clean,
isotropic extreme type-II $\kappa \to \infty$ superconductors. This work
clarifies an important issue: the unpinned vortex liquid is always incoherent
with no phase coherence in any directions for all anisotropies. Previous claims
of a disentangled vortex liquid for isotropic superconductors based on
simulations, are due to finite size effects. We explicitly show that the
effective vortex-line tension vanishes precisely at the superconducting phase
transition in zero magnetic field. This loss of line tension is accompanied by
an abrupt change in the connectivity of the vortex tangle across the
superconductor. We also obtain results indicating that the connectivity of the
vortex tangle changes in a similar way even in finite magnetic field, and
suggest that this could also be associated with a genuine phase-transition.
