### Log-space Algorithms for Paths and Matchings in k-trees

Bireswar Das, Samir Datta & Prajakta Nimbhorkar
Reachability and shortest path problems are \NLC\ for general graphs. They are known to be in \Log\ for graphs of tree-width $2$ \cite{JT07}. However, for graphs of tree-width larger than $2$, no bound better than \NL\ is known. In this paper, we improve these bounds for $k$-trees, where $k$ is a constant. In particular, the main results of our paper are log-space algorithms for reachability in directed $k$-trees, and for computation of shortest and longest...