# Are there any known W[3] or W[3]-hard problems?

We are currently working on a variant of domination parameter and we have shown that it is in W[3] with regard to parameterized complexity. To show it is W[3]-complete, we must show the problem is W[3] hard i.e, reduce an already known W[3] hard problem to ours. But unlike W[1] and W[2], where many famous problems are proved those classes, surprisingly we have not come across a single problem that is W[3] hard and not even in just W[3]. Of course there is the general W[t] case which we can go for, but any result for W[3] in particular would help a lot.

There are a few examples in the answer to Natural complete problems in higher levels of the W-hierarchy. In particular, the W[3]-complete problem $$p$$-HYPERGRAPH-(NON)-DOMINATING-SET may be useful for your proof.