The complexity of planarity testing
Information and Computation
Space efficient algorithms for directed series-parallel graphs
Journal of Algorithms
Undirected connectivity in log-space
Journal of the ACM (JACM)
Directed Planar Reachability Is in Unambiguous Log-Space
ACM Transactions on Computation Theory (TOCT)
Planar and Grid Graph Reachability Problems
Theory of Computing Systems - Special Issue: Computation and Logic in the Real World; Guest Editors: S. Barry Cooper, Elvira Mayordomo and Andrea Sorbi
Space complexity of perfect matching in bounded genus bipartite graphs
Journal of Computer and System Sciences
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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.