You are given a Graph G and an integer k.
The question is: Does G contain a vertex set X of size at most k such that deleting X results in a graph of degree at most 1?
Design an FPT (or a kernelization) algorithm for this problem and argue why it is correct.
Hint: Observe that vertices of higher degree must be "dealt with" somehow.
I do not exactly know where to start. I suppose that some reduction rules can be applied first, but not so sure what those can be (probably something that "deals with" vertices of higher degree.