The proof that Exponential Time Hypothesis (ETH) is true, would imply that P!=NP among other implications (like solvability of SAT in sub-exponential time is not possible in the worst case).But, if proven that ETH is false, how would it impact the Complexity Hierarchy and what would be the implications of the proof. Results, that immediately follow from the ETH falseness (based on our current knowledge)?
Implication of Exponential Time Hypothesis falseness?
cc.complexity theory
One such result is by Megiddo and Vishkin. They proved that minimum dominating set in tournaments is in $QP$. Additionally, they showed that tournament dominating set has P-time algorithm if and only if SAT has subexponential time algorithm. Therefore, ETH falseness implies that tournament dominating set is in $P$ which seems unlikely.