  We obtain a number of lower bounds on the running time of algorithms solving
problems on graphs of bounded treewidth. We prove the results under the Strong
Exponential Time Hypothesis of Impagliazzo and Paturi. In particular, assuming
that SAT cannot be solved in (2-\epsilon)^{n}m^{O(1)} time, we show that for
any e > 0; {\sc Independent Set} cannot be solved in (2-e)^{tw(G)}|V(G)|^{O(1)}
time, {\sc Dominating Set} cannot be solved in (3-e)^{tw(G)}|V(G)|^{O(1)} time,
{\sc Max Cut} cannot be solved in (2-e)^{tw(G)}|V(G)|^{O(1)} time, {\sc Odd
Cycle Transversal} cannot be solved in (3-e)^{tw(G)}|V(G)|^{O(1)} time, For any
$q \geq 3$, $q$-{\sc Coloring} cannot be solved in (q-e)^{tw(G)}|V(G)|^{O(1)}
time, {\sc Partition Into Triangles} cannot be solved in
(2-e)^{tw(G)}|V(G)|^{O(1)} time. Our lower bounds match the running times for
the best known algorithms for the problems, up to the e in the base.
