Longest paths in Planar DAGs in Unambiguous Logspace
  We show via two different algorithms that finding the length of the longest path in planar directed acyclic graph (DAG) is in unambiguous logspace UL, and also in the complement class co-UL. The result extends to toroidal DAGs as well. 
Nutan Limaye, Meena Mahajan, Prajakta Nimbhorkar