Vertex coloring with an upper bound on the degree of the nodes
Yes, it's still NP-hard. 3-COL is still NP-complete for planar degree 4 graphs [1].




Dailey, D. P. (1980), "Uniqueness of colorability and colorability of planar 4-regular graphs are NP-complete", Discrete Mathematics 30 (3): 289–293, DOI:10.1016/0012-365X(80)90236-8