Reachability in K3, 3-Free Graphs and K5-Free Graphs Is in Unambiguous Log-Space

We show that the reachability problem for directed graphs that are either K3,3-free or K5-free is in unambiguous log-space, UL coUL. This significantly extends the result of Bourke, Tewari, and Vinodchandran that the reachability problem for directed planar graphs is in UL coUL. Our algorithm decomposes the graphs into biconnected and triconnected components. This gives a tree structure on these components. The non-planar components are replaced by planar components that maintain the reachabilty properties. For K5-free graphs we also need a decomposition into fourconnected components. A careful analysis finally gives a polynomial size planar graph which can be computed in log-space. We show the same upper bound for computing distances in K3,3-free and K5-free directed graphs and for computing longest paths in K3,3-free and K5-free directed acyclic graphs.

• Type: Conference
• Year: 2009
• Where: FCT
• Authors: Thomas Thierauf, Fabian Wagner
• Keywords: Applied Computing, FCT 2009, Planar Graph, Reachability Problem, UL CoUL