Abstract
Directed reachability (or briefly reachability) is the following decision problem: given a directed graph G and two of its vertices s , t , determine whether there is a directed path from s to t in G . Directed reachability is a standard complete problem for the complexity class NL. Planar reachability is an important restricted version of the reachability problem, where the input graph is planar. Planar reachability is hard for L and is contained in NL but is not known to be NL-complete or contained in L. Allender et al. [2009] showed that reachability for graphs embedded on the torus is logspace-reducible to the planar case. We generalize this result to graphs embedded on a fixed surface of arbitrary genus.
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