Consider the following language: $$ L = \{ G | G \text{ has a VC of size at most } \log n \} $$
Does $L\in P$ or $L\in NPC$?
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Sign up to join this communityConsider the following language: $$ L = \{ G | G \text{ has a VC of size at most } \log n \} $$
Does $L\in P$ or $L\in NPC$?
If you solve Vertex Cover with the simple branching algorithm, you achieve an FPT running time of $2^k \text{poly}(n)$, where $k$ is an upper bound for the solution you are looking for.
Substituting $k$ for $\log n$ gives you the answer you are looking for.