The isomorphism problem for planar graphs is known to be efficiently solvable. For planar 3-connected graphs, the isomorphism problem can be solved by efficient parallel algorithms, it is in the class AC^1.

In this paper we improve the upper bound for planar 3-connected graphs to unambiguous logspace, in fact to ... more >>>

We report progress on the \NL\ vs \UL\ problem.
\begin{itemize}
\item[-] We show unconditionally that the complexity class $\ReachFewL\subseteq\UL$. This improves on the earlier known upper bound $\ReachFewL \subseteq \FewL$.
\item[-] We investigate the complexity of min-uniqueness - a central
notion in studying the \NL\ vs \UL\ problem.
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We prove that Perfect Matching in bipartite planar graphs is in UL, improving upon
the previous bound of SPL (see [DKR10]) on its space complexity. We also exhibit space
complexity bounds for some related problems. Summarizing, we show that, constructing:
1. a Perfect Matching in bipartite planar graphs is in ... more >>>