# Is the clique problem polynomial-time solvable still in unit disk graphs allowing different sized disks?

Clark et al. proved that the clique problem is polynomial-time solvable in unit disk graphs. Does anyone know if this result holds still if the disks are allowed to be different sizes? Or do such "non-unit disk graphs" in fact constitute all graphs, and thus the clique problem is NP-hard again? (I've been able to draw some of the impossible unit disk graphs found here with different sized disks.)

EDIT: as stated in the comments, disk graphs are a strict subset of graphs. In this paper the authors give an example: $$K_{3,3}$$ is not a disk graph.

• Interesting question, I don't know. But disk graphs do not constitute all graphs.
– Juho
Oct 15 '21 at 16:05
• As a general tip, a good place to start searching with these questions is to take a look at the ISGCI: the page on the class of disk graphs has clique as 'unknown'. Oct 15 '21 at 17:09