In the analysis of problem 1439B is it is written that

If d(u) > k, remaining vertices will form a subset that every vertex have at least k neighbors in the subset, so we'll print this subset as answer.

If d(u) = k − 1, we consider u and all neighbors of u as candidate for clique of size k. then we erase u and all edges attached to it.

So, what we do when d(u) = k? Maybe there is typo here and first condition should be d(u) ≥ k?