# Finding the minimum vertex cover of planar graph given the planar representation

The minimum vertex cover problem is $$NP$$-hard for the planar graph of degree at most $$3$$. However, the minimum vertex cover can be easily found in some certain types of planar graph, given the planar representation. For example, the planar graph that every face boundary is a cycle of even length.

Is there any proof that shows the $$NP$$-hardness of the minimum vertex cover of the (general) planar graph, given its planar representation as an auxiliary input?