  We prove that unless Exponential Time Hypothesis (ETH) fails, deciding if
there is a homomorphism from graph $G$ to graph $H$ cannot be done in time
$|V(H)|^{o(|V(G)|)}$. Combined with the reduction of Cygan, Pachocki, and
Soca{\l}a, our result rules out (subject to ETH) a possibility of
$|V(G)|^{o(|V(G)|)}$-time algorithm deciding if graph $H$ is a subgraph of $G$.
For both problems our lower bounds asymptotically match the running time of
brute-force algorithms trying all possible mappings of one graph into another.
Thus, our work closes the gap in the known complexity of these fundamental
problems.
